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    "# Intuition behind Eigen Values and Eigen Vectors\n",
    "\n",
    "\n",
    "**Eigen vectors** are vectors which are fixed in direction under a given linear transformation. The scaling factor of these Eigen vectors are called **Eigen values**.\n",
    "\n",
    "These **Eigen-pairs**(Eigen value and corresponding vector) are analogous to the roots of a polynomial. For example, consider cubic polynomials in a single variable, having 3 distinct roots. The general structure of these polynomials remain the same, but **rooted** at different points.\n",
    "![Screenshot 2024-08-15 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S970u/t+Ze9Qdr7pV/6Pwzv7PmfOE31vUvtpr3dVu34vc9/vtqq6urM68OjRtvvNE666yzrKamJnPGstasWWMde+yx+jU/SaVS1hNPPGF9/OMftyZMmKBrc0877TTrjjvusPbu3Wvelbtnn33Wd591IK2trdYVV1xh3XvvveaMf8Xjceull17S1/vcc8+Zs/t66623rM5f5PTfbWVlpXX99ddbW7duNa8CKKR0Oq23bL2PbU7nh0tNTY3V2NhoNTc3Wy0tLXrMSSaT+t+MXK7Vq39/g9hPdXW1abkTxNh4dS1BjLGfrkXxU4z9Fhs/xTiosfGiH8ZiZ15dC2OxsyDG2G+x8aKf8vJyq6qqyhzlbzg+04o1W625Vy3X20t1O8zZjFz6ueOZX1jzqxZaC277oDnTzYvPxVjszKtrYSx2FsQY+y02fopxUGPjRT+Mxc68uhbGYmdBivE+c3Ykxs2XDx8WM0fGhjq5eVVUQuEikc4tpKpSwu3y3X9u63st0nRSr0Xa2b+uNlVT7lqpw+X8w3tVJXZskyeXbTQHw0NNoasyzL01NTXJSy+9JLNnzzZn/OFvf/ubrmj99Kc/rdcLTaVS8o1vfENuueUWvanjXKkqzOeff15PMWz761//qvv3s0ceeURXvPqZ+vlSUzV/4AMfkCeffFKeeuopSae7p83J9vrrr8vPf/5z+c53vqNj/+yzz8qGDRvkvPPO039HAAqrr0pLp8rLwVZkAgAAAMBgdGRPsetiDdKOZGaK3WLWHwUAAOjXPndcH7uosscUuMrrbzwvDTo5GpaQmjc31PnHVKL0z+tk1S7zJlvWWqSiEkEqQZpKyjs/d7AcX2LeYzS9ulr+X3OvZOwQU1PJLliwQC6++GKZOHGiPqeSWkuWLJGzzjpLzj77bH3OjVWrVsn9999vjtwpKSmRAw44oGsKXDWF4pw5c+Sggw7SSbWOju61JgZDJd7uvvtuncTL1traKmVlZebIf+rr63UCfv78+eaMP6m/pzvvvFMee+wx/fPktPagSmyr93zpS1+S8vJyfW769Oly3XXXqSpv+cUvfiGJREKfB1AYmS/1eLsGKQAAAAAMRryjO0EaLco/QZpIZZ4dREmQAgAA9GufO673T+31MHjXRln6UOdNVTiSSYyq/KiuslFVpPXyqzf2mjfayuSdpx+vq0gtvanq0UPl0qPHmNeNVJM8+sC/ZPK47jUVhou9xqhdPWQnBn/3u991JU3dUMkvp6rBXJ188sl6zc3TTz/dnFHruL4tb731lixcuFAnUAdLJVSvvPJKufXWW/Vntj+/2l5++WXfrkMaj8dl5cqVctppp5kzI9/evXvl6aeflq9//et6DV6bSnyrv3NVzbxnzx5zFkAh2ONftt7HAAAAAFAIiawK0li0V+VCDhKpzBfnY5FivQcAAEDf9kmQxnb2LAld9+prsiwcyUyrqx8Um4fF6rgoIn+/e538sz1zyhabebBc/864WJ03ZelkQt752UNlfq9ixN1vrpObtoVl1oEHmDPeU0nJV199Va666iqdBEwmkzq5pqYxnTVrlvzgBz/ompJWJUnt6iG1qao/vyYIbeo633zzTfne976nKw0/+MEPmldEf9YVK1boqXhV9ap6r0qwffOb35Rp06bpcyr5q6apzf7c9pY93a7fqKlnTzzxRMcKV5VgVAv8fvzjH9fT1ioqqfzRj35U5s2bJ2vXrtXn/EQltisrK81RN/W/uaKi/H8xAjB49viXrfexzek8AAAAAOQjkexeMsmLKXapIAUAAOjfPndcO3e3mFanXRvkV0uaJKRuqlT1aJdQ5v9CRZ2vrZE7X+1d2VYm7zzjBJnWERer43D50rH7Vo/+8dev6aTrMQdNMCe9p6oM586dKz/+8Y/lvvvu09PJqmlMP/axj0ldXZ187WtfG7HJp4ceekhP13rKKafoNSo/+9nPSiQSMa+KPPDAA/q1e+65R37961/rKWmfeOIJnUjdtGmTXHjhheadI4u6dpX8Pfjgg82ZntT0yNdee61OeD/44IM6TiqJ3NjYqI/VWquHHXaYebd/xGIxqaqq0n9Xagpl286dO2XdunVy+OGHy+jRo81ZAIWQSwWp03kAAAAAyEdHyps1SO0KUtYgBQAA6N8+d1xTJ3RX5b1W87z8rqiP6lFFNU0V6TMP18s/45nTttjMo+SHH47KKZ89tI+1R1/X1aOStuSMY6ebs95TU5OqKtLHH39cJ5p++MMfyvHHHy+TJ0827xi5zj//fF3BpJJ/anpdtYaqSgLaVIJQVceqtVRfeOEFXTWrpuUdNWr4pzTOl0qMPvfcczrx65ScsNf8VFWkX/jCF+Tee++VmpoaOfXUUx3X//QzldBV0++qNWJVEhVA4eRSQQoAAAAAXsqeYjfqpoLUJEijERKkAAAA/dnnjmvG5APk+dX1ItvWyU9+0yoSMmuP7iOrinT7avnJ87ukZ460SI4/5yL575N7TaHb2iC/+O36zj8ekncdcaDMnNyrutRjKpGmEqXnnHOOnlJ20qRJ5hXvNTc3y7nnnqv/m9mbSuh98pOf3Of8cccdp6ta3VDVhpdeeqn+b6tphNUUwjaVEFTT7qrPP3Xq1B6ViV5TiTwV396f0WlTCT9V7ZkL9d9QFcGDSfKOGTNGTy+sqIpR9d8ciIrdl770pX2utb9NTWNcKA0NDfLLX/5SbrnlFjnyyCPNWQCFYv/vOlvvYwAAAAAohOwEqRcVpEyxCwAA0L8+77iSyYSs+suf5OlwSCcyM8+H+3hIrE7pKtKoPL/0RVm+uXu9hL6l5MXHn5NfqepRKy0Xntb3NKleKy4ulkMPPVReeeUV2bWr5xqrXho/frz8/ve/76pCsje1ZqaqZOx9/sUXX9RTp7ql/rsqCfjkk0/Kxo0bzdkMNS3r7Nmz5bXXXpPW1lZz1ntqbc/t27fv8xmdtlzXeN2yZYu+/lymx1VJYZW0Xb16tTnTP1Wh+ZOf/KTP63XaVPK5EHbs2KGvRa0Fq6pfARSe/b/rbL2PbU7nAQAAACAfiY6sCtIiFwnSZELvY0XFeg8AAIC+9XnHdeTMSfJA86HqCbCEuh4Y9/Uw2FTShdVapNvkm3e8JKv2mpf6EF//ilz7B1U1aMmHT5wpJx46JfNCgW3YsEFPtbtnzx7dHqnUlLk33nijfPSjH5Vt27aZs5nEnpo2eO3atdLU1GTOZqjkoEoUqgRp9p8ZadQ6nGeeeaauirWrvMrKyqS6urqrOletM2tTP7NqauFjjjlGJ6ITicwvCCNBS0uL/OhHP9LTJr/jHe8wZwEUmj22ZOt9bHM6DwAAAAD5sCtIYy6qR5WuKXapIAUAAOiX413XNy96pxwydbSk0503VqnUAEnSzFqk4R3r5LP3vCGv9VGouHvDa3Ll91+SjSHR/X79E8ebVwpLrVupEmRqzc4ZM2bo9SgVVY2okqYjiUqQqrVUe1NrVK5fv15OOOEEmTZtmjmbSbTV19fraX8VlUBVf4/qs4+06idVqamuOXtTyeCzzjqrqzpXrbtqU2uzlpeXy/vf/3755z//qd+rfhba29vNO/xJ/Z3ddtttenrgo48+2pwVvY6umkYZQOHYY0u23scAAAAAUAh2gtTN+qOKPcVuMWuQAgAA9Kvfu66bPnmiTB0TkXQqIVYqKZZKKOqHxb0eGIdUNY2qIo1K+PVX5OM/eEJufeItefpfO+XFV9bL0vuXyzu/WytPh0JSPi6m+y20u+++W6/JqRKic+bM0YnDY489VifLVPLsz3/+84irAFJTBX/84x+X0047TSdL1YN7tW7mb3/7W3n00Uflkksu0Z/zW9/6ltx///3y97//XebPny8VFRV67U51rCpKV65cGYjqJ5XwVJtKHKpk9+bNm2XRokVdf8eq+lJNYawqh1UFqvo7b2xsNH966KnrUMlpleTuK+mikqO/+tWvdOWomhLapj6jSvDmMiUxgNypcbH32EilKAAAAIChYCdIiyNFep+vjlRmBi0qSAEAAPrXb4J05uQx8v8+N08OnhwTKxkXK9UhVtpUk3YlStWmMqSd/09PtRuRcHOz3PNQjXzh/z0qF93+d/nuU7s7X7bk4Kmj5LbPv0v3W2iTJk2Se+65R1cMHnLIIfoh9+mnn67X6XzsscfknHPOGbIH30VFRXpqWC+ohOd73vMe+c///E/9GdXUuio5qpJ/F154of5vTZgwQW6//XY58MAD9aYSa+rP/OY3v9GJwzPOOMP0NjKptU7PPvtsPXWwqqz8j//4D/25ly9frpOJv/zlL/W6nZFIRGbOnCnvete75Ic//KEcccQRUllZaXoZOjfddJP+WTvppJN0/D/0oQ/pnwf1GdRnUdR1/+xnP5MrrrhCZs2apd9vb9FoVDZt2iQlJSX6vQAKQ/3b1vvLC319mUFxOg8AAAAA+ehI2QlSjypISZACAAD0a8C7LpXMvOeq98gHjz9Q0h3tku5KlKqK0pSuKrUstVliiZmyNtTZrUo+dm7qrHS+70PvqJBfX33GkCRHFZUAffXVV3Vi0E6Eqmla16xZI1/4whd08myoqKSmSl56QX0WVQn7i1/8QifXdu/erStI1fS6dkLtyiuvlGeffVaOOuoo86dELrjgAh2P8847ryseI9XEiRPlkUceyfzMZW2qglbF4ic/+YmMGZP5OVPJ4Z/+9Kc6eZpdlTmUbrjhhn2uVW3qM6jPoqifx+uuu67P96nt6quv1u8DUDj2GJrNabwc6eMoAAAAAH+Jd6T0vjjqMkGatKfYLdZ7AAAA9G3Qd11f//jx8uPPnSTvOvgASSfadLLUSqqpdzuy9p2bmopXtdW0vMm4vPuQcfLjz79Tvv6JE0xPAAD4j/2FhGy9jwEAAACgELqn2HWXIO0wFaRMsQsAANC/nO66Tjx0itz62fly/zWnyiXvnS3zZ4+RA0eJFKXjko636r06Vucvee/Bne87TW793Lv0nwMAwM9yqSAFAAAAAC95lSBNmDVImWIXAACgf3nddalpcj/13sN0svTBr71Xnrz5A7Lilg/pvTpW59XrQzWdLgAAbuVSQUplKQAAAAAvdXheQcoUuwAAAP0J7dixw3dPedW6mpWVleYIAAD0p7a2Vle7RqNRval1jcPhcFdV7GArYRsaGqSiosIc5S+I/SxdulQWLVpkjvIXxNh4dS1BjLGfrkXxU4z9Fhs/xTiosfGiH8ZiZ15dC2OxsyDG2G+x8aKfefPmyeLFi/XmxnB8pq//73p5taFFjpkxWm4+/yBzNiOXfi548BK9//hRH5Hzj/yQbtu8+FyMxc68uhbGYmdBjLHfYuOnGAc1Nl70w1jszKtrYSx2FqgYqwSp37a6ujoLAIChlE6n9Zat97Ff1dTUWI2NjVZzc7PV0tJixeNxK5lMWqlUKqfP4NW/v0Hsp7q62rTcCWJsvLqWIMbYT9ei+CnGfouNn2Ic1Nh40Q9jsTOvroWx2FkQY+y32HjRT3l5uVVVVWWO8jccn2nRbc9Yc69abn2h+u/mTLfB9hPviFvzqxbqbcnzD5iz3bz4XIzFzry6FsZiZ0GMsd9i46cYBzU2XvTDWOzMq2thLHYWpBi7m7cDAICA6KvScrCVlwAAAADghhdT7CbM9LpKlDVIAQAA+kWCFAAAAAAAABhGCQ8SpPb6o0oxa5ACAAD0iwQpAAAAAAAAMIzsBGmUClIAAIAhQYIUAAAAAAAAGEZ2gjTmUQVpLEKCFAAAoD8kSAEAAAAAAIBh5MUUuz0rSJliFwAAoD8kSAEAAAAAAIBh1J0gLdL7fCSSCdNiil0AAICBkCAFAAAAAAAAhlEimdJ7N2uQZk+xW0yCFAAAoF8kSAEAAAAAAIBhlExZeu9mDdLsKXaLWYMUAACgXyRIAQAAAAAAgGHSnshUjypuKkjjybhpMcUuAADAQEiQAgAAAAAAAMMkbtYfVYrdVJAms6fYLTYtAAAA9IUEKQAAAAAAADBMEh3dFaSxaJFp5S6RTJgWU+wCAAAMhAQpAAAAAAAAMEyyK0jdrUHanSCNUUEKAADQLxKkAAAAAAAAwDCJe1RB2p61BmksGjMtAAAA9IUEKQAAAAAAADBM4h1ZFaRRFxWkrEEKAAAwaCRIAQAAAAAAgGEST3ZXkBZ7NMUua5ACAAD0L7Rjxw7LtH1j9+7dUllZaY4AAEB/amtrJRQKSTQa1VskEpFwOKzP2dtgNDQ0SEVFhTnKXxD7Wbp0qSxatMgc5S+IsfHqWoIYYz9di+KnGPstNn6KcVBj40U/jMXOvLoWxmJnQYyx32LjRT/z5s2TxYsX682Nof5ML23YK99Y9pZu/+Djs+WoilG6bRtsP79d/bAse/3/dPs3H7tL77N58bkYi515dS2Mxc6CGGO/xcZPMQ5qbLzoh7HYmVfXwljsLEgxDq1Zs8Z3CVIAADB4e/fulRkzZkhxcbHeVIK0qKgo5wRpfX29J19QCmI/d911l1xyySXmKH9BjI1X1xLEGPvpWhQ/xdhvsfFTjIMaGy/6YSx25tW1MBY7C2KM/RYbL/qZNm2aXHPNNXpzY6g/01OrG+U//ucfun3/lxfIUTPG6rZtsP389Km7ZGnNQ1IaLZEnvvSwOdvNi8/FWOzMq2thLHYWxBj7LTZ+inFQY+NFP4zFzry6FsZiZ4GKsaog9dtWV1dnAQCAwampqbEaGxut5uZmq6WlxYrH41YymbRSqZSVTqfNuwbm1b+/QeynurratNwJYmy8upYgxthP16L4KcZ+i42fYhzU2HjRD2OxM6+uhbHYWRBj7LfYeNFPeXm5VVVVZY7yN9Sf6S8vbrLmXrVcb29u2m3OdhtsP1WP/cyaX7XQOuv2j5kzPXnxuRiLnXl1LYzFzoIYY7/Fxk8xDmpsvOiHsdiZV9fCWOwsSDFmDVIAAAAAAABgmMQ70qYlUhzN/1Fd3KxBWlxUrPcAAABwRoIUAAAAAAAAGCaJZMq0RGKRItPKXSJpEqSRqN4DAADAWVaCtEVee/gWueWWzPbcJnMaAAAAAAAAQEFkV5DGXFSQ2gnSWCSm9wAAAHDWddfV8tpf5I1Dr5Drrruuc/ukyJLnpMG8BgAAAAAAAMB78Y6sCtJo/hWkcTtByhS7AAAAA+pKkI6ac56cN2eUORon444wTQAAAAAAAAAFEU92V5CWFruYYtdegzRCghQAAGAgfczboaba/ZnsPOndUmHOAAAAAAAAAPCeXUFaFA7pfb7sClLWIAUAABhYrwRpgzx3y19EzrhO3j3NnAIAAAAAAABQEAlTQVriYnpdxa4gZQ1SAACAgXUnSPe8Jr+7pV4qrztP5owx5wAAgCvpdFq2bNkiTU1NYlmWOds/9b7t27fLtm3b9J8HAAAAEFzxjsw9f3G0j4necpCwK0hZgxQAAGBAXXdeDS8vl7XyjNx7yy1yi96ekwbzGgAAyJ1KbjY2NkpDQ4PU19fr9kBJUvW6el9dXZ1s2LBBt0mSAgAAAMFlT7Ebi7irILWn2I0xxS4AAMCAuhKkFSdfJ9ddl72xBikAAG60trbKpk2bzJHoSlJVGeqUJFXnt27dqt9nU8dtbW3mCAAAAEDQxM0Uu55VkEaoIAUAABiIuzsvAADgqKSkRCZOnGiORFKplLz99tt9Jknt5OjmzZv1+2zjx4+X0tJScwQAAAAgaBKmgtTtGqRx1iAFAAAYNBKkAAAUSCQSkRkzZsiUKVPMmb6TpE7J0alTp8r06dMlHOafawAAACCouipII24rSDv0njVIAQAABpbXndfbzQ1y//MPyvUPf1cu/sVl8oGf/Zuc+ePz9F4dq/PqdfU+AAD2Z0VFRVJRUaGTnbbsJKlaX9QpOVpeXk5yFAAAAAi4rjVIXU6xG0/G9b6YNUgBAAAGlNOd1wv1L+vk52d+/R/yy+fvl5qGF2VrfLukI2kpKonovTpW59Xr6n3q/erPAQCwv1JJTpXs7CtJ+q9//UvvSY4CAAAA+6d4R6aCNBbJf4rdjlSmelSJUUEKAAAwoEE/ea169Kdy3e+/LTVv/1OKYmEJR4sk3HnjFo6GJRTp3Ioye3WsXysukqKSIp0sVX+u6i8/Mz0BALD/sZOkvafb3bNnjznKUK+THAUAAAD2H4lk5suSxS4qSOPJzPqjSnGEBCkAAMBAQjt27MgsgOZATZN70x+rZH1zvYSLQiLhzi0UEv3cNhRWTX0saq909WaJXlqt8/+zUpakk2mZPa5SvvHBa2T6+IrMWxzs3r1bKisrzREAAIVnrwca0v+wZahz2cc2p/ODoabUVdPpbtmyxZzpppKjajreXJOjtbW1+nqi0aje1Nqnqg91zt4Go6GhQf/33QpiP0uXLpVFixaZo/wFMTZeXUsQY+yna1H8FGO/xcZPMQ5qbLzoh7HYmVfXwljsLIgx9ltsvOhn3rx5snjxYr25MdSf6Qv3rJW3m+Oy4LCxcu0HZpqz3QbTz674brl0+Vd0+/MnfFLeN/tU3c7mxediLHbm1bUwFjsLYoz9Fhs/xTiosfGiH8ZiZ15dC2OxsyDFuN8EqUqOXvfQd2RryzZV+tJ5xjJ50JCEisymHsDq57idr/R+/qp7ziRKM0nSlEwpnSQ/OO+b/SZJSZACAIKs899e2bBhQ49pdVVic8aMGTJ+/HhzZvBUglT92eLiYr2pBKla+zTXBGl9fb0n//4GsZ+77rpLLrnkEnOUvyDGxqtrCWKM/XQtip9i7LfY+CnGQY2NF/0wFjvz6loYi50FMcZ+i40X/UybNk2uueYavbkx1J/p7JuekE07WuUjJ02X7y46zpztNph+tuzeKuf998W6/Y2zr5EPHrVQt7N58bkYi515dS2Mxc6CGGO/xcZPMQ5qbLzoh7HYmVfXwljsLEgx7rdERVWONrY0dbZCcuV7L5FHr35Inv/mE7LiPx+VpZ//bznr8DN00tNK61JRkxDNop7H2g9ni0J66t2trU26XwAA/ERVhdpVpLbex17oKzmqdHR06PPqdQAAAAD7j3hH5neDWDT/NUjjybhpiRSzBikAAMCAHBOktz76U1m/vU7nOL99ztfkond/QiaOmdB5HJLiSFQOOXC2fPX9X5LzjvmQnj7X0uvJOzxIVsWlJlEajoR1vz/4423mRX9444035Ljjjuu6zptuusm8AgDYH9jjf7bex245VY7aksmkbNy4kSQpAAAAsB+xE6TFkdyW2siWyFqDNMYapAAAAAPq887rhfqX5dHVj+vE5hfP+JwsnHu6hDPz6PYwpmS0fHbBJ+Vds04SK53WU+k65UgzSVK1zzQOnXawrGuqy7w2zFRy9O6775aVK1fqaqHW1lY9b/Fll10mbW1t5l0AgCDLpYI0n8rSvpKjas3RI488Uu9tJEkBAACA/UsiqasOpMRNBWmKBCkAAEAu+kyQPvjCwxIKh2ThUWfI+Sd+RIr7ubGaMnaSXHDS+aaKtJ8Maedp/YqVlncffJJ85MQPSqQ4ol8abjU1NXLrrbfKsmXL9HFpaaksWLBAVq1apR9mAwCCL5cK0lwrS52So2oBcVVBqvaTJ082r2SSpEy3CwAAAOwf7ARpcdRNBWmHaalKVBKkAAAAA9nnzuvt5gZ5/q1aKYuVyifmnSdjyw4wr6gEpyVbdm6VtkR3VaWacveEWcfIv8+/QKyUqr7pPNlnjrTztbQl6aTIx046RyaPnSjHVc6VrXu3mdeHz0UXXaSrgdTetn79epk/f77MnDnTnAEABFkuFaSDpf58U1OTY3I0HM78M6z206dP75EkVe9Xf27r1q2urwMAAACAP9nT6yqxCGuQAgAADJV9EqRPr31O7z987Pvl8PJDdNu2vrFOLv/VV+TBv/9BkqmkOasWkY/J++acLqVFsb6rSDsP9bPdztfOPe79cvysY3ViVWlq2a73frJixQp56KGH5Oqrr9bVpACA4MulgnSw1DTtmzZt6pEcnTp1ao/kqM0pSar+vJr6HQAAAEDwxDsy1aNKzFUFafcUu1SQAgAADGyfO69XGl6XsmipnHnU6VJa3J0cjHfE5U8v/1Xqd22U/37mHvlX41vmlYzZUyrl4+84V6yUmmq380SPHKmpHu187cw5p+u1S22jSrvbw+2mm27SD8Mvv/xyeeCBB+Twww83rwAAgi6XCtLBVnSq6XNHjRpljjKVo+Xl5fskR23qfO/pdseMGSPFxTzgAAAAAIIobqbXVWIu1iBNsAYpAABATvZ5QlvftFE+cOxCOaxX9ejrm9bKg7UPSzgalnYrLo+99uQ+305735z3SGlRiXlw3LnZO7VPW3LWkWfIEdMOU2/vUhotMa3hd8MNN+hrX7lypdx2221y2WWX6eofAEDw5VJBOtjKUpUgVVO1jx8/fp9pdZ0UFRXJtGnTZNKkSfrPqT+v+gEAAAAQPIkeU+zmX0Eaz1qDNMYUuwAAAAPa586rafcOOeOo0/QapDZVPfrs2pXSlm6XUFFYb/9b+3tZv7XevCNjnypSLZMhTacsWXjUGTImq2LU6vy/dVt6VqL6gZpW9+KLL5bq6mpZtmyZOTv01LSKqqp19+7d5gwAoFDUF2R6V4YOtlK0Pyq5OXv2bJkxY8aAyVFbJBKRyspK/edIjgIAAGB/UFLiny/QD6XsCtJiN1PsZlWQMsUuAADAwPa583rfnFPlyF5Vnm9t2yD/+8LDmeRoOKS3tlS7rFr3jx5rkfauIs1soqfXfddBJ8lR04/oWntU2d26R556fYU5Gj4qCXn22WfL9u3d66Gqyp1jjz1W1q9fb84Mvc2bN8vPf/5zGTt2bFdlk73NmjVLr5XqN+l0Wv72t7/JeeedJwcccICceuqp8sQTT3iSZACAQrLH12y9jwEAAAAUxrhx40xr/xLvUUGa/xS78WTctEiQAgAADMY+CdKFx75XDigbY47UzLiWvLzxVZ0QzTw87jzZuYXCYXlq7QrZtqcp80Yju4pUZUf12qNJSz4w90yZMHq8eVemevTF+lfkb689Y84MDzWFbkNDgznq1tTUJC+99JKu3hkuzc3N8vrrr2clmzPb22+/Ld/+9rdl/vz55p3+oGKpks0//elP5Tvf+Y7s3LlTHnroIfnLX/4idXV15l0A4E/2GJut97HN6TwAAACA/MRiMf1F8N7LHam2Omd/oVFtvb/kPpLFO7LXIHVRQZq1DBZrkAIAAAxsnzuvionTTCujcVej/PnVx3RCNFP8aW5IOw9Xb1kjL21YrZOdNvUttTOOXJCpIk11vtK5nTjzWDlh1jE9qkf3tO2VR19+XCaOmWDODA81ne6CBQv0lLoTJ07U59TN95IlS+Sss87SN93DIZFISDKZ1NWj2dS1LV++XD760Y/qder8QiULVDL0qaee0gnSY445Rk8lqX65UdMU79q1y7wTAPzJftiSrfexzek8AAAAgPyo5wennHKKOeq2YcMGPUNVa2tr15caH3nkka5nOCNdIplVQRrN/zlPImsN0kg4YloAAABwsk+CtDXRalqZ6tGat17UiVA9ta56IGw/E1YPkotC8qdX/io79jabkxkHTzlIPnbCOZJOpsXq3M457gMy+YBJ5tWMNZvWyiOvPC6Vk2aYM8Pnoosu0nv74XhZWZk+/t3vfjdsN9zFxcX7JGfVLwGPPfaYnH766fqXAz/ZsmWL3HPPPfKhD31Ipk3rTrKfe+65snbtWjnuuOPMGQDwJ/thS7bexwAAAAC8pSpB1fOPyy+/XL761a+as93UDF9jxozRX3APoh5rkEbyryCNmzVIS6IxvQcAAED/9rnzamnba1qZ6tFlLyzXa49mFX/qts6VhkOyqu4f8kLdSz2qSGOdN2PvPfJUKZGYzJ91opx00Ak9qkd3t+2Rh1/4k+7j6IojzVnvqfUwX331Vbnqqqvk1ltv1RWZ8Xhcr+up1vD8wQ9+IKlU5pt6KklqPxxX25133um7m2+VaNyzZ48cdljPNWLV51LftPz0pz8t999/v75+9b5vfvObOlmpzhWairNK3qp1W++66y4dX1VF+otf/ELHHAD8zv6STLbexwAAAAC8d80118iLL76onyn0ppbsWb16ddf9epCm11XiCW8qSO01SIuLmF4XAABgMPZJkE4alamYVNWjK9b+XVZv7qN6VFPHneeLQvKX1X+T5r07zfmMw8oPkUtO+3d5/9z3yfh91h59WR599XF9dNrh7868UAArV66UuXPnyo9//GO577775I033tBJvI997GP6BvtrX/uar6ap7Y9K5KopbI8++uh9Htg/8MADehoaVcH561//Wurr6+WJJ56Q6667TjZt2iQXXniheWfhrF+/Xg499FB57rnnZM6cOfr48ccfl1WrVsl//dd/6SQuAPiZ/QWZbL2PbU7nAQAAAORGzdx15plnmqN9qecL48aN65piVy2RpL7kHpg1SLMqSN2tQZqZYjcWoYIUAABgMPa585oyerK8WP+KvL39bXng+WU6AdozMWpk8qM6efrUv1bIM2tXSirdfVMXKYrIxadeIB84fqGEsxJ6Tbu3y4P/eFjXm8476ESZPr4i80IBnHzyybqKVCXqdu7cKT/84Q/l+OOPl8mTJ5t3jBxqzY3XX39dKir2jZf6xUAlUNW6qS+88IKukFXT8I4aNcq8o/C2bt2qp9mdMmWKTtaq9UdVnK+44gpdwaoSpwDgZ/Y30rP1PrY5nQcAAACQH/X8pi833HBDj1m+PvrRj+pZq9Q6pEEQ78iqII24WYM0M8VucSSq9wAAAOhfaMeOHfuUwaxrqpOat/4p//PcEikqiUhYTbHb15fYOv+krrhJWVI5drrcfN435NCpB5sX95VMJeU3q5bJf/31Dv1nfnj+jXJC5THm1W67d++WyspKc+SemuL12muv1dWialpdtb5nITQ3N8tnPvMZefjhh82Z/qmpY1T15+GHH27OOPvDH/4gf/rTn+S2225znPpX/fc/97nPyYIFC+Tqq682Z52pilRVTTtYN954o/7FpC/qur785S/Ls88+qxPTNvWNTpXAVUnT66+/nqQCAN+yq0Kzxyl1biSMW7W1tfLkk0/qf+cikc5/t8NhvdnXPtjPoMZsL9beDmI/Tz/9tJx66qnmKH9BjI1X1xLEGPvpWhQ/xdhvsfFTjIMaGy/6YSx25tW1MBY7C2KM/RQb9XzkuOOOkwcffFCeeeYZ+dGPfqRnolJrj6r7WmXz5s2SSCRk5syZ8t3vfldmz56tn2n84x//kNdee02/Rz37UdWo/VWkDsZQxuaV5lHy1Jaxuv35w7ZISdG+ieLB9PO3tlVSl2yQ8eED5NxRfX9+Lz4XY7Ezr66FsdhZEGPst9j4KcZBjY0X/TAWO/PqWhiLnQUqxipB2td27T3ftN7xzdOsed9/r/XOW8605t+60Jpf1cfWef6dPzzTmve991r/ce911padWy0n/6x72Vpw8/utEzr7/c/7b+zzv6u2uro68ye8kU6nrZ/+9KfW+973PmvrVufr86vOXwqsr3/969all15qtba2mrP76vxFwbrmmmusz3/+81ZLS4s5OzR+85vfqMyC9eyzz5ozGU1NTdZZZ5014LUDAPJXU1NjNTY2Ws3NzXr8j8fj+t+OVCql/w0cLK/+/Q1iP9XV1ablThBj49W1BDHGfroWxU8x9lts/BTjoMbGi34Yi515dS2Mxc6CGGO/xUbdu9577709nh/YzxSynzWo19R7ej9/UMrLy62qqipzlL+hjM2v/rbOmnvVcr21tHeYsz0Npp9rlt2gn9N9esnl5sy+vPhcjMXOvLoWxmJnQYyx32LjpxgHNTZe9MNY7Myra2EsdhakGDsubvC1D18lsyfOknRHZk02tel5cXsLqcqUzq0oLKvq/yHVT/1SduxtNi9mqHVHX337dbl5+Y+kJd4qB0+YJV856wrzauGp6WnVVC179uzR7ZFm79698uabb8rUqVOlpKTEnN3X6tWr9XvUNye3bdtmzg6NQw45RDp/ETFH+xro2gFguHX9W5el97HN6TwAAAAA76hqADVLlVpSqK2tTZ9btmyZ3p9wwgl6P9LFE91T7JZE859iN941xW5hZk0DAAAIGscEqXLDh74iB5ZNknRHSk+Jm0mSqs28oUtIQmoW3khY/m/1X+SyJV+W+1b+r17L9Jk3npOqP/1MPv0/X5T12+rkwNGT5YYPf8X8ucJTU7K8+OKLcv7558uMGTOkpqZGn1eL+zutb+E3av3UTZs26akTnaZJbGlpkfr6ejn33HP18dq1a/Xfl/qcQ/Eg/9BDD9Xl0K+++qo5k9HQ0KDXJj3jjDMGPcUjAAwHNUb1Hqecxi3GMwAAAGBoqKV+KioqpKysTN+Hq2TpzTff7Lj80EgTT2aeTRWFQxLu3PKVSGUSpDESpAAAAIPSb4J0+vgK+f55N8jssZWZJGnnTZuV7pUoVZu+f1NJ0s6tKCz1u96Wn/ztTlm85Er58m+/Ib+tWabff/DEWXLL+d/S/Rba3XffLbfeeqtOiM6ZM0emTZum17T45z//qasx//znP4+YB9zt7e06AdpbKpWSb33rW3L//ffL3//+d5k/f77+pWHu3Ln6WFWUrly5ckg+5wEHHCBf+MIX5Ne//rVeL0Qln9X6ID/72c/kwgsvlHe/+93mnQDgT+rftt5fKBmKL5gAAAAAyNx7X3TRRXLnnXfuk/xUSVL7fv2RRx7xZN0rv0h0ZCpIYy6qR5WEXUFaRIIUAABgMPpNkCoqmXnnJ/+fLDzsdEnFU5LuSIuVSktaVZSaZGn3PvNnVD7O6vz/VMJUUe8968gzpPri24YkOapMmjRJ7rnnHp1cVNO/qiTh6aefLk8++aQ89thjcs4554yYBOm4ceP09LXjx483ZzLC4bBMmDBBbr/9djnwwAP1pn6JeM973iO/+c1vdCJYVW4OFVVBetNNN8l3vvMdXe163nnn6ZhfddVVEolEzLsAwJ/Uvwm9/10YKf9OAAAAACOdmj1rf2RXkBZHBnxE1y87QUoFKQAAwOAM+u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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "E6kSmViruiBy"
   },
   "source": [
    "### **So, what does this mean?**\n",
    "\n",
    "If you are working with an invariant line/plane/hyperplane, the amount of transformation that can be performed to the surrounding space is limited. So, the eigen vectors, being fixed, act like skewers that restrict the linear transformations and hold it in place.\n",
    "\n",
    "So, verrrryyyy roughly, the eigen values are a measure of the distortion induced by the linear transformation, and the eigen vectors specify the direction of orientation of the distortion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "En41C_AYqr5Y"
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import sympy as sp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0hR3Dq_hniNm"
   },
   "source": [
    "### Eigenvalue and Eigenvector Calculation for a 2x2 Matrix\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "7rT6LquAq3Eq"
   },
   "outputs": [],
   "source": [
    "def compute_eigenvalues_2x2(a, b, c, d):\n",
    "    trace = a + d\n",
    "    determinant = a * d - b * c\n",
    "\n",
    "    discriminant = trace**2 - 4 * determinant\n",
    "    sqrt_discriminant = math.sqrt(discriminant)\n",
    "\n",
    "    lambda1 = (trace + sqrt_discriminant) / 2\n",
    "    lambda2 = (trace - sqrt_discriminant) / 2\n",
    "\n",
    "    return lambda1, lambda2\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "WunC_0el7x9c"
   },
   "outputs": [],
   "source": [
    "def compute_eigenvector_2x2(a, b, c, d, eigenvalue):\n",
    "    # Solve (A - lambda I) v = 0\n",
    "    if b != 0:\n",
    "        x = 1\n",
    "        y = (eigenvalue - a) / b\n",
    "    else:\n",
    "        x = 0\n",
    "        y = 1\n",
    "\n",
    "    return x, y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "GPaxVNCRtVhE"
   },
   "source": [
    "### Eigenvalue and Eigenvector Calculation for a 3x3 Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "ULso29J7tXR5"
   },
   "outputs": [],
   "source": [
    "def compute_eigenvalues_3x3(A):\n",
    "    a, b, c = 1, -np.trace(A), np.linalg.det(A)\n",
    "    p = np.poly(A)\n",
    "\n",
    "    eigenvalues = np.roots(p)\n",
    "\n",
    "    return eigenvalues\n",
    "\n",
    "def compute_eigenvectors_3x3(A, eigenvalues):\n",
    "    eigenvectors = []\n",
    "\n",
    "    for eigenvalue in eigenvalues:\n",
    "        I = np.eye(3)\n",
    "        M = A - eigenvalue * I\n",
    "        _, v = np.linalg.qr(M)  # Use QR decomposition for simplicity\n",
    "        eigenvectors.append(v[:, 0])  # Take the first vector from QR\n",
    "\n",
    "    return eigenvectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "TgGsNGattbz4",
    "outputId": "5214b15f-b1aa-4c2d-9512-82de01b1cc38"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues: [1.00000657+0.00000000e+00j 0.99999671+5.69015387e-06j\n",
      " 0.99999671-5.69015387e-06j]\n",
      "Eigenvector for eigenvalue (1.0000065704250627+0j): [-6.57042506e-06+0.j  0.00000000e+00+0.j  0.00000000e+00+0.j]\n",
      "Eigenvector for eigenvalue (0.9999967147874662+5.6901538690326425e-06j): [-6.57042407e-06+0.j  0.00000000e+00+0.j  0.00000000e+00+0.j]\n",
      "Eigenvector for eigenvalue (0.9999967147874662-5.6901538690326425e-06j): [-6.57042407e-06+0.j  0.00000000e+00+0.j  0.00000000e+00+0.j]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[2, 6, 10],\n",
    "              [3, 8, 13],\n",
    "              [-2, -6, -10]])\n",
    "\n",
    "\n",
    "\n",
    "eigenvalues = compute_eigenvalues_3x3(A)\n",
    "\n",
    "eigenvectors = compute_eigenvectors_3x3(A, eigenvalues)\n",
    "\n",
    "print(f\"Eigenvalues: {eigenvalues}\")\n",
    "for i, vector in enumerate(eigenvectors):\n",
    "    print(f\"Eigenvector for eigenvalue {eigenvalues[i]}: {vector}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ql7I-uwLlgQh"
   },
   "source": [
    "## Using numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "DI5UgI6ZqCZo"
   },
   "source": [
    "### Eigenvalues and Eigenvectors Calculation\n",
    "\n",
    "In this section, we compute the eigenvalues and eigenvectors of the matrix \\( A \\) using NumPy's `linalg.eig` function.\n",
    "\n",
    "The matrix \\( A \\) is defined as:\n",
    "\n",
    " A = \\begin{pmatrix} 4 & -2 \\\\ 1 & 1 \\end{pmatrix} \\\n",
    "\n",
    "The function `np.linalg.eig(A)` returns two outputs:\n",
    "1. **Eigenvalues**: The scalars \\( \\lambda \\) that satisfy the equation \\( A \\mathbf{v} = \\lambda \\mathbf{v} \\).\n",
    "2. **Eigenvectors**: The vectors \\( \\mathbf{v} \\) associated with each eigenvalue.\n",
    "\n",
    "The eigenvalues and eigenvectors are displayed below.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "vOXk3WBSkq1-",
    "outputId": "0ebbf989-2ad0-4fa5-e24b-2cd7b16ce822"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues:\n",
      "[3. 2.]\n",
      "\n",
      "Eigenvectors:\n",
      "[[0.89442719 0.70710678]\n",
      " [0.4472136  0.70710678]]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[4, -2],\n",
    "              [1, 1]])\n",
    "\n",
    "eigenvalues, eigenvectors = np.linalg.eig(A)\n",
    "\n",
    "print(\"Eigenvalues:\")\n",
    "print(eigenvalues)\n",
    "\n",
    "print(\"\\nEigenvectors:\")\n",
    "print(eigenvectors)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TPKV4dAmqPsQ"
   },
   "source": [
    "### Visualize Matrix Transformation and Eigenvectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "DsenLH5Eqa_r"
   },
   "source": [
    "This section visualizes how the matrix \\( A \\) transforms a grid of vectors and plots the eigenvectors.\n",
    "\n",
    "1. **Matrix Transformation**:\n",
    "   - We create a grid of points and apply the matrix transformation to visualize how the matrix \\( A \\) affects these points. The blue arrows represent the transformed grid.\n",
    "\n",
    "2. **Eigenvectors**:\n",
    "   - The red arrows represent the eigenvectors of the matrix \\( A \\). These vectors point in directions where the matrix transformation acts as simple scaling (stretching or compressing).\n",
    "\n",
    "The plot helps to understand how eigenvectors remain in the same direction while being scaled by their corresponding eigenvalues.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 717
    },
    "id": "7o0VQYKUnzvy",
    "outputId": "7e8772db-3014-4f14-c50f-f31c43a2d6ef"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-2, 2, 10)\n",
    "y = np.linspace(-2, 2, 10)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "grid = np.vstack([X.ravel(), Y.ravel()])\n",
    "\n",
    "transformed_grid = np.dot(A, grid)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlim(-5, 5)\n",
    "ax.set_ylim(-5, 5)\n",
    "ax.set_aspect('equal')\n",
    "\n",
    "ax.quiver(grid[0, :], grid[1, :], transformed_grid[0, :] - grid[0, :], transformed_grid[1, :] - grid[1, :], angles='xy', scale_units='xy', scale=1, color='blue', alpha=0.5)\n",
    "\n",
    "for i in range(len(eigenvalues)):\n",
    "    eigenvector = eigenvectors[:, i]\n",
    "    ax.quiver(0, 0, eigenvector[0], eigenvector[1], angles='xy', scale_units='xy', scale=1, color='red', label=f'Eigenvector {i+1}')\n",
    "\n",
    "ax.set_title('Matrix Transformation and Eigenvectors')\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.legend()\n",
    "ax.grid(True)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "qoKZGmG2bgX1"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_IptZs0USr0y"
   },
   "source": [
    "# **GRADIENT DESCENT PROBLEMS**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "bTChUmCiauFm",
    "outputId": "0f3e089d-1e35-4fc0-bc41-8223379b8c39"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0: x = 3.6000, f(x) = 23.0400\n",
      "Iteration 10: x = -3.4359, f(x) = 1.6437\n",
      "Iteration 20: x = -4.4692, f(x) = 0.5859\n",
      "Iteration 30: x = -4.9032, f(x) = 0.3008\n",
      "Iteration 40: x = -5.1438, f(x) = 0.1833\n",
      "Iteration 50: x = -5.2972, f(x) = 0.1235\n",
      "Iteration 60: x = -5.4037, f(x) = 0.0889\n",
      "Iteration 70: x = -5.4820, f(x) = 0.0671\n",
      "Iteration 80: x = -5.5421, f(x) = 0.0524\n",
      "Iteration 90: x = -5.5896, f(x) = 0.0421\n",
      "Final value: x = -5.6246, f(x) = 0.0352\n"
     ]
    }
   ],
   "source": [
    "def f1(x):\n",
    "    return (1/4)*(x**2) + 3*x + 9\n",
    "\n",
    "def derivative_f1(x):\n",
    "    return ((1/2)*x + 3)**2\n",
    "\n",
    "def gradient1(x):\n",
    "    return derivative_f1(x)\n",
    "\n",
    "x = 10\n",
    "x1 = None\n",
    "step_size = 0.1\n",
    "iterations = 100\n",
    "\n",
    "for i in range(iterations):\n",
    "    grad1 = gradient1(x)\n",
    "    x = x - step_size * grad1\n",
    "    if i % 10 == 0:\n",
    "        print(f\"Iteration {i}: x = {x:.4f}, f(x) = {f1(x):.4f}\")\n",
    "\n",
    "print(f\"Final value: x = {x:.4f}, f(x) = {f1(x):.4f}\")\n",
    "# Correction: remove the square operation in the derivative function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "xMurdw_XRpnB",
    "outputId": "a74c9986-ea5d-43cf-d329-d4f5bba49994"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0: x = -7.6333, f(x) = 4496.4599\n",
      "Iteration 10: x = -33.4699, f(x) = 0.2846\n",
      "Iteration 20: x = -33.9333, f(x) = 0.1267\n",
      "Iteration 30: x = -34.2503, f(x) = 0.0651\n",
      "Iteration 40: x = -34.4814, f(x) = 0.0369\n",
      "Iteration 50: x = -34.6577, f(x) = 0.0225\n",
      "Iteration 60: x = -34.7968, f(x) = 0.0146\n",
      "Iteration 70: x = -34.9095, f(x) = 0.0098\n",
      "Iteration 80: x = -35.0026, f(x) = 0.0069\n",
      "Iteration 90: x = -35.0809, f(x) = 0.0050\n",
      "Final value: x = -35.1414, f(x) = 0.0038\n"
     ]
    }
   ],
   "source": [
    "def f2(x):\n",
    "    return (1/144)*(x**4) + x**3 + 54*(x**2) + 1296*x + 11664\n",
    "\n",
    "def derivative_f2(x):\n",
    "    return (1/36)*(x**3) + 3*x**2 + 108*x + 1296\n",
    "\n",
    "def dderivative_f2(x):\n",
    "    return (1/12)*(x**2) + 6*x + 108\n",
    "\n",
    "def gradient2(x):\n",
    "    return dderivative_f2(x)\n",
    "\n",
    "x = 10\n",
    "x1 = None\n",
    "step_size = 0.1\n",
    "iterations = 100\n",
    "\n",
    "for i in range(iterations):\n",
    "    if x1 is not None:\n",
    "        grad2 = gradient2(x1)\n",
    "    else:\n",
    "        grad2 = gradient2(x)\n",
    "    x1, x = x, x - step_size * grad2\n",
    "    if i % 10 == 0:\n",
    "        print(f\"Iteration {i}: x = {x:.4f}, f(x) = {f2(x):.4f}\")\n",
    "\n",
    "print(f\"Final value: x = {x:.4f}, f(x) = {f2(x):.4f}\")\n",
    "# Correction: replace second derivative with first, compute gradient at the current step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "L_VpxFoiVYFR"
   },
   "source": [
    "#**Parameters**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "A5-r9E0Ea1T7"
   },
   "outputs": [],
   "source": [
    "# We will use this code for demonstrations of different function and different step sizes\n",
    "# This code snippet in this notebook need not to be sent to students before tutorials, only made for explaning things\n",
    "import time\n",
    "\n",
    "# def f(x):\n",
    "#     return x**2\n",
    "# def derivative_f(x):\n",
    "#     return 2*x\n",
    "\n",
    "def f(x):\n",
    "    return x**4 - 6*x**3 + 25*x + 30\n",
    "def derivative_f(x):\n",
    "    return 4*x**3 - 18*x**2 + 25\n",
    "\n",
    "initial_x = 10\n",
    "iterations = 100\n",
    "learning_rate = 0.001\n",
    "\n",
    "# Store the values for visualization\n",
    "x_values = []\n",
    "f_values = []\n",
    "\n",
    "x = initial_x\n",
    "start_time = time.time()\n",
    "\n",
    "for i in range(iterations):\n",
    "    x_values.append(x)\n",
    "    f_values.append(f(x))\n",
    "\n",
    "    grad = derivative_f(x)\n",
    "    x = x - learning_rate * grad\n",
    "\n",
    "end_time = time.time()\n",
    "total_time = end_time - start_time\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 751
    },
    "id": "dzSolUmRa8lg",
    "outputId": "3caafc0b-4c40-4461-b980-82496b758b72"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-9-a486294016c7>:26: MatplotlibDeprecationWarning: Setting data with a non sequence type is deprecated since 3.7 and will be remove two minor releases later\n",
      "  line.set_data(x_values[i], f_values[i])\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_img98d1312204a34f709bf40dba425d073d\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider98d1312204a34f709bf40dba425d073d\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim98d1312204a34f709bf40dba425d073d.set_frame(parseInt(this.value));\">\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim98d1312204a34f709bf40dba425d073d.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim98d1312204a34f709bf40dba425d073d.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim98d1312204a34f709bf40dba425d073d.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim98d1312204a34f709bf40dba425d073d.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim98d1312204a34f709bf40dba425d073d.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim98d1312204a34f709bf40dba425d073d.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim98d1312204a34f709bf40dba425d073d.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim98d1312204a34f709bf40dba425d073d.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim98d1312204a34f709bf40dba425d073d.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select98d1312204a34f709bf40dba425d073d\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_98d1312204a34f709bf40dba425d073d\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio1_98d1312204a34f709bf40dba425d073d\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_98d1312204a34f709bf40dba425d073d\"\n",
       "             >\n",
       "      <label for=\"_anim_radio2_98d1312204a34f709bf40dba425d073d\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_98d1312204a34f709bf40dba425d073d\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_98d1312204a34f709bf40dba425d073d\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_img98d1312204a34f709bf40dba425d073d\";\n",
       "    var slider_id = \"_anim_slider98d1312204a34f709bf40dba425d073d\";\n",
       "    var loop_select_id = \"_anim_loop_select98d1312204a34f709bf40dba425d073d\";\n",
       "    var frames = new Array(100);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA+gAAAJYCAYAAADxHswlAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "bAIAAAAAAEZ5mQ4AAAAAAAAo6AAAAAAAOAUKOgAAAAAAToCCDgAAAACAE6CgAwAAAADgBCjoAAAA\\\n",
       "AAA4AQo6AAAAAABOgIIOAAAAAIAToKADAAAAAOAEKOgAAAAAADgBCjoAAAAAAE6Agg4AAAAAgBOg\\\n",
       "oAMAAAAA4AQo6AAAAAAAOAEKOgAAAAAAToCCDgAAAACAE6CgAwAAAADgBCjoAAAAAAA4AQo6AAAA\\\n",
       "AABOgIIOAAAAAIAToKADAAAAAOAEKOgAAAAAADgBCjoAAAAAAE6Agg4AAAAAgBOgoAMAAAAA4AQo\\\n",
       "6AAAAAAAOAEKOgAAAAAAToCCDgAAAACAE6CgAwAAAADgBCjoAAAAAAA4AQo6AAAAAABOgIIOAAAA\\\n",
       "AIAToKADAAAAAOAEKOgAAAAAADgBCjoAAAAAAE6Agg4AAAAAgBOgoAMAAAAA4AQo6AAAAAAAOAEK\\\n",
       "OgAAAAAAToCCDgAAAACAE6CgAwAAAADgBCjoAAAAAAA4AQo6AAAAAABOgIIOAAAAAIAToKADAAAA\\\n",
       "AOAEKOgAAAAAADgBCjoAAAAAAE6Agg4AAAAAgBOgoAMAAAAA4AQo6AAAAAAAOAEKOgAAAAAAToCC\\\n",
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       "ADgBCjoAAAAAAE6Agg4AAAAAgBOgoAMAAAAA4AQo6AAAAAAAOAEKOgAAAAAAToCCDgAAAACAE6Cg\\\n",
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       "RK5CYII=\\\n",
       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        anim98d1312204a34f709bf40dba425d073d = new Animation(frames, img_id, slider_id, 200.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as animation\n",
    "import time\n",
    "\n",
    "# Set up the plot\n",
    "fig, ax = plt.subplots(figsize=(10, 6))\n",
    "x_range = np.linspace(-10, 10, 400)\n",
    "y_range = f(x_range)\n",
    "\n",
    "# Plot the function\n",
    "ax.plot(x_range, y_range, label=r'$f(x) = x^2$', color='black', linestyle='--')\n",
    "line, = ax.plot([], [], 'ro', label='Gradient Descent Path', markersize=8)  # Larger marker size for visibility\n",
    "text = ax.text(0.05, 0.9, '', transform=ax.transAxes)\n",
    "\n",
    "# Set plot limits and labels\n",
    "ax.set_xlim(-10, 10)\n",
    "ax.set_ylim(0, 110)\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('f(x)')\n",
    "ax.legend()\n",
    "ax.grid(True)\n",
    "\n",
    "# Animation function\n",
    "def animate(i):\n",
    "    line.set_data(x_values[i], f_values[i])\n",
    "    text.set_text(f'Iteration: {i+1}\\nTime Elapsed: {total_time:.2f} seconds')\n",
    "    return line, text\n",
    "\n",
    "# Create the animation\n",
    "ani = animation.FuncAnimation(fig, animate, frames=len(x_values), interval=200, repeat=False)\n",
    "\n",
    "plt.close(fig) # Extra static plot was coming\n",
    "\n",
    "# Display the animation in Notebook\n",
    "from IPython.display import HTML\n",
    "HTML(ani.to_jshtml())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "background_save": true
    },
    "id": "U1M_VqodbBkP"
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "provenance": []
  },
  "kernelspec": {
   "display_name": "ai511",
   "language": "python",
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  "language_info": {
   "codemirror_mode": {
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