Class 04.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[3 2]\n",
      " [4 1]]\n"
     ]
    }
   ],
   "source": [
    "# Este es el caso para una matriz donde se puede descomponer como A = autovectores * diag(lambdas) * autovectores_INV\n",
    "\n",
    "A = np.array([[3, 2], [4, 1]])\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "autovalores, autovectores = np.linalg.eig(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 5. -1.]\n"
     ]
    }
   ],
   "source": [
    "print(autovalores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.70710678 -0.4472136 ]\n",
      " [ 0.70710678  0.89442719]]\n"
     ]
    }
   ],
   "source": [
    "print(autovectores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Esta es la descomposición de una matriz 2x2\n",
    "\n",
    "A_calc = autovectores.dot(np.diag(autovalores)).dot(np.linalg.inv(autovectores))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[3. 2.]\n",
      " [4. 1.]]\n"
     ]
    }
   ],
   "source": [
    "print(A_calc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.2  0.4]\n",
      " [ 0.8 -0.6]]\n"
     ]
    }
   ],
   "source": [
    "A_inv = np.linalg.inv(A)\n",
    "print(A_inv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[3 2]\n",
      " [2 3]]\n"
     ]
    }
   ],
   "source": [
    "# Este es el caso para una matriz simetrica, donde se puede descomponer como B = autovectores * diag(lambdas) * autovectores_T\n",
    "\n",
    "B = np.array([[3,2], [2,3]])\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ True  True]\n",
      " [ True  True]]\n"
     ]
    }
   ],
   "source": [
    "# Observamos que B coincide con su transpuesta\n",
    "\n",
    "print(B == B.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "autovalores_B, autovectores_B = np.linalg.eig(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5. 1.]\n"
     ]
    }
   ],
   "source": [
    "print(autovalores_B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.70710678 -0.70710678]\n",
      " [ 0.70710678  0.70710678]]\n"
     ]
    }
   ],
   "source": [
    "print(autovectores_B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[3. 2.]\n",
      " [2. 3.]]\n"
     ]
    }
   ],
   "source": [
    "B_calc = autovectores_B.dot(np.diag(autovalores_B)).dot(autovectores_B.T)\n",
    "print((B_calc))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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