svd.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8177b07c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy.matrices import Matrix, eye, ones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "efe4d83a",
   "metadata": {},
   "outputs": [],
   "source": [
    "M = ((1, 2, 0),\n",
    "     (0, 0, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "51f60f23",
   "metadata": {},
   "outputs": [],
   "source": [
    "M = Matrix(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1520f448",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 2 & 0\\\\0 & 0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1, 2, 0],\n",
       "[0, 0, 1]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7019a07f",
   "metadata": {},
   "outputs": [],
   "source": [
    "U, Σ, Vt = M.singular_value_decomposition()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "db659ab3",
   "metadata": {},
   "outputs": [],
   "source": [
    "V = Vt.transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1939e959",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0, 1],\n",
       "[1, 0]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ada4525c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0\\\\0 & \\sqrt{5}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1,       0],\n",
       "[0, sqrt(5)]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Σ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "557d065a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 1\\\\\\frac{\\sqrt{5}}{5} & \\frac{2 \\sqrt{5}}{5} & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[        0,           0, 1],\n",
       "[sqrt(5)/5, 2*sqrt(5)/5, 0]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a5387019",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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   "file_extension": ".py",
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