AL002.000_Tr_mat.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sympy import * # Librería para operaciones simbólicas\n",
    "from ubogsla18p import * # Librería personal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$b=$$\\left[\\begin{matrix}b_{0}\\\\b_{1}\\\\b_{2}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b=Matrix(symbols('b0:3'))\n",
    "imprimir('b=',b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$A=$$\\left[\\begin{matrix}a_{00} & a_{01} & a_{02}\\\\a_{10} & a_{11} & a_{12}\\\\a_{20} & a_{21} & a_{22}\\\\a_{30} & a_{31} & a_{32}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# asignando matrices de variables\n",
    "A=Matrix(symbols('a:4:3')).reshape(4,3)\n",
    "imprimir('A=',A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Transformaciones\n",
    "\n",
    "Una __transformación__ (__función__) $T$ de un conjunto $A$ en un conjunto $B$, representada por $T:A \\rightarrow B$ asocia cada elemento $a$ de $A$ en un elemento $b$ único de $B$ llamado __imagen__ de $a$ bajo $T$.\n",
    "* $A$ se llama el dominio de $T$.\n",
    "* $B$ se llama el codominio de $T$.\n",
    "* La __imagen__ de $T$ es el conjunto de todas las imágenes de los elementos de $A$, $Im(T)=\\{T(a) \\mid a \\in A\\}$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Transformación matricial\n",
    "[Nakos, Sec 5.1]\n",
    "\n",
    "Una transformación $T:\\mathbb{R}^n \\rightarrow \\mathbb{R}^m$ dada por \n",
    "$$T(\\vec{x})=A\\vec{x}$$\n",
    "donde $A$ es una matriz de tamaño $m \\times n$ y $x \\in  \\mathbb{R}^n$, se conoce como una __transformación matricial__. $T$ aveces la denoto $T_A$ o $A$ aveces la denoto $A_T$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$T($$\\left[\\begin{matrix}b_{0}\\\\b_{1}\\\\b_{2}\\end{matrix}\\right]$$)=$$\\left[\\begin{matrix}a_{00} b_{0} + a_{01} b_{1} + a_{02} b_{2}\\\\a_{10} b_{0} + a_{11} b_{1} + a_{12} b_{2}\\\\a_{20} b_{0} + a_{21} b_{1} + a_{22} b_{2}\\\\a_{30} b_{0} + a_{31} b_{1} + a_{32} b_{2}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def T(x):\n",
    "    return A*x\n",
    "\n",
    "imprimir('T(',b,')=',T(b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$T($$\\left[\\begin{matrix}1\\\\2\\\\3\\end{matrix}\\right]$$)=$$\\left[\\begin{matrix}a_{00} + 2 a_{01} + 3 a_{02}\\\\a_{10} + 2 a_{11} + 3 a_{12}\\\\a_{20} + 2 a_{21} + 3 a_{22}\\\\a_{30} + 2 a_{31} + 3 a_{32}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c=Matrix([1, 2, 3])\n",
    "imprimir('T(',c,')=',T(c))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Con las columnas de la identidad $I_3=\\begin{bmatrix}1&0&0\\\\0&1&0\\\\0&0&1\\end{bmatrix}$ se pueden recuperar las columnas de $A$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$I_3=$$\\left[\\begin{matrix}1 & 0 & 0\\\\0 & 1 & 0\\\\0 & 0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "imprimir('I_3=',eye(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$T($$\\left[\\begin{matrix}1\\\\0\\\\0\\end{matrix}\\right]$$)=$$\\left[\\begin{matrix}a_{00}\\\\a_{10}\\\\a_{20}\\\\a_{30}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c0=eye(3).col(0)\n",
    "imprimir('T(',c0,')=',T(c0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$T($$\\left[\\begin{matrix}0\\\\1\\\\0\\end{matrix}\\right]$$)=$$\\left[\\begin{matrix}a_{01}\\\\a_{11}\\\\a_{21}\\\\a_{31}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c1=eye(3).col(1)\n",
    "imprimir('T(',c1,')=',T(c1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$T($$\\left[\\begin{matrix}0\\\\0\\\\1\\end{matrix}\\right]$$)=$$\\left[\\begin{matrix}a_{02}\\\\a_{12}\\\\a_{22}\\\\a_{32}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c2=eye(3).col(2)\n",
    "imprimir('T(',c2,')=',T(c2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imagen de una matriz bajo transformaciones matriciales\n",
    "\n",
    "Dada la transformación matricial $T_A:\\mathbb{R}^n \\rightarrow \\mathbb{R}^m$ podemos definir la trantransformación $T_A^*$ de tal forma  que la imagen de una matriz $B=\\begin{bmatrix} v_0 & v_1 & \\cdots & v_{k-1} \\end{bmatrix}$ bajo la transformación matricial $T^*_A$ es \n",
    "\\begin{align}\n",
    "T_A^*(B)&=\\begin{bmatrix} T_A(v_0) & T_A(v_1) & \\cdots & T_A(v_{k-1})\\end{bmatrix}\\\\\n",
    "&=\\begin{bmatrix} Av_0 & Av_1 & \\cdots & Av_{k-1}\\end{bmatrix}\\\\\n",
    "&=AB\n",
    "\\end{align}\n",
    "\n",
    "### Teoremas\n",
    "* Si $T_A$ es una transformación matricial entonces $$A=T_A^*(I)$$ \n",
    "\n",
    "$$A=\\begin{bmatrix} \n",
    "T_A\\left(\\begin{bmatrix} 1 \\\\ 0 \\\\ \\vdots \\\\ 0 \\end{bmatrix}\\right) & \n",
    "T_A\\left(\\begin{bmatrix} 0 \\\\ 1 \\\\ \\vdots \\\\ 0 \\end{bmatrix}\\right) & \n",
    "\\cdots &\n",
    "T_A\\left(\\begin{bmatrix} 0 \\\\ 0 \\\\ \\vdots \\\\ 1 \\end{bmatrix}\\right) \n",
    "\\end{bmatrix}$$\n",
    "\n",
    "\n",
    "* Sea una transformación $T:\\mathbb{R}^n \\rightarrow \\mathbb{R}^m$.\n",
    "  * $T$ es una transformación matricial _sii_  $T^*(I) x= T(x)$ para todo $x \\in \\mathbb{R}^n$\n",
    "\n",
    "\n",
    "Ejercicio:\n",
    "* Encontrar la imagen la matriz $B=\\begin{bmatrix} 0 & 0 & 0.5 & 1 & 1 & 0 \\\\ 0 & 1 & 1.5  & 1 & 0 & 0  \\end{bmatrix}$ bajo la transformación matricial $T_A\\left(\\begin{bmatrix} x \\\\ y  \\end{bmatrix}\\right)=\\begin{bmatrix} y/2 \\\\ 2x  \\end{bmatrix}$. \n",
    "\n",
    "Respuesta:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$T^*($$\\left[\\begin{matrix}0 & 0 & 0.5 & 1 & 1 & 0\\\\0 & 1 & 1.5 & 1 & 0 & 0\\end{matrix}\\right]$$)=$$\\left[\\begin{matrix}0 & \\frac{1}{2} & 0.75 & \\frac{1}{2} & 0 & 0\\\\0 & 0 & 1.0 & 2 & 2 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A=Matrix([[0, 0, 0.5,1,1,0],[0, 1,1.5,1,0,0]])\n",
    "\n",
    "def T1(v):\n",
    "    return Matrix([v[1]/2,2*v[0]])\n",
    "\n",
    "imprimir('T^*(',A,')=',fun_cols_mat(T1,A))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Encontrar la matriz $A$ de la transformación $T_A\\left(\\begin{bmatrix} x \\\\ y  \\end{bmatrix}\\right)=\\begin{bmatrix} y/2 \\\\ 2x  \\end{bmatrix}$\n",
    "\n",
    "Respuesta:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$T^*($$\\left[\\begin{matrix}1 & 0\\\\0 & 1\\end{matrix}\\right]$$)=$$\\left[\\begin{matrix}0 & \\frac{1}{2}\\\\2 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "I2=eye(2)\n",
    "imprimir('T^*(',I2,')=',fun_cols_mat(T1,I2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ejercicos:\n",
    "* Para las siguientes transformaciones encuentre la matriz $A_T$, si $T$ es una transformación matricial, de lo contrario demuestre que no es una transformación matricial.\n",
    "  * $T\\left(\\begin{bmatrix}x_1\\\\x_2\\end{bmatrix}\\right)=3\\begin{bmatrix}x_1\\\\x_2\\end{bmatrix}$\n",
    "  \n",
    "  * $T\\left(\\begin{bmatrix}x_1\\\\x_2\\end{bmatrix}\\right)=\\begin{bmatrix}x_1\\\\0\\end{bmatrix}$\n",
    "  * $T\\left(\\begin{bmatrix}x_1\\\\x_2\\end{bmatrix}\\right)=\\begin{bmatrix}x_1\\\\5\\end{bmatrix}$\n",
    "  * $T\\left(\\begin{bmatrix}x_1\\\\x_2\\end{bmatrix}\\right)=\\begin{bmatrix}x_1\\\\5x_2\\end{bmatrix}$\n",
    "  * $T\\left(\\begin{bmatrix}x_1\\\\x_2\\end{bmatrix}\\right)=\\begin{bmatrix}x_1\\\\5+x_2\\end{bmatrix}$\n",
    "\n",
    "Respuesta del último ejercicio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$T^*($$\\left[\\begin{matrix}1 & 0\\\\0 & 1\\end{matrix}\\right]$$)=$$\\left[\\begin{matrix}1 & 0\\\\5 & 6\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def T2(v):\n",
    "    return Matrix([v[0],5+v[1]])\n",
    "\n",
    "A=fun_cols_mat(T2,eye(2))\n",
    "imprimir('T^*(',eye(2),')=',A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\left[\\begin{matrix}1 & 0\\\\5 & 6\\end{matrix}\\right]$$\\left[\\begin{matrix}x_{0}\\\\x_{1}\\end{matrix}\\right]$$=$$\\left[\\begin{matrix}x_{0}\\\\5 x_{0} + 6 x_{1}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=Matrix(symbols('x0:2'))\n",
    "imprimir(A,x,'=',A*x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Entonces $T\\left(\\begin{bmatrix}x_1\\\\x_2\\end{bmatrix}\\right)=\\begin{bmatrix}x_1\\\\5+x_2\\end{bmatrix}$ no es una transformación matricial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algunas transformaciones de $\\mathbb{R}^2$ en $\\mathbb{R}^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$v=$$\\left[\\begin{matrix}x\\\\y\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v=Matrix(symbols('x y'))\n",
    "imprimir('v=',v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$B=$$\\left[\\begin{matrix}0 & 0 & 0.5 & 1 & 1 & 0\\\\0 & 1 & 1.5 & 1 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B=mat('0 0;0 1;0.5 1.5;1 1;1 0;0 0').T\n",
    "imprimir('B=',B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x93a6170>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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M7HJi/+MNSmge5O5FZtYKeN/Mlsd/IkmFz4AO7r7fzK4DphK7k226ugGY5+6J\nP72l0+dZY2huRiot5qWZnUEsmO5z973VtZ9krhSqcruMMNtGJdS+zKwP8AowzN13HG1396L431uB\nKcSWbymp0933uvv++OMZQKaZtQizbTLrTDCKckv0JH6elUmHuRlKGszNSqXJ3Awr5fPSzDKJBcKf\n3H1yBUOim5/JOFESP+FRF1gNdOL/Tnj0LDdmKF89WfL3sNsmuc4OxL69fXG59oZAo4TH84EhKayz\nDf/3BcX+wLr4Z5tWn2d8XBNix3cbpuLzjO+jI8c+MZryuRmyzpTPzZB1pnxuVlZjGs1LA14Dnj/O\nmMjmZ9IOH3lqbpdRXXU+CjQHXjYzgBKP3UGxNTAl3lYXeN3d301hnTcB3zezEqAYGOWxmZJunyfA\ncOA9dz+QsHnSPk8ze4PYFTEtzGwD8BixGzqmzdwMWWfK52bIOlM+N0PUCCmel3EDgVuBPDNbHG97\niNgPAJHPT93mQkREAvpGs4iIBBQKIiISUCiIiEhAoSAiIgGFgoiIBBQKIiISUCiIiEjg/wM22EAe\nPHPT7wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x4567370>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mat(B,0,0,2,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Escalonar ejes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\left[\\begin{matrix}2 & 0\\\\0 & 1\\end{matrix}\\right]$$\\left[\\begin{matrix}x\\\\y\\end{matrix}\\right]$$=$$\\left[\\begin{matrix}2 x\\\\y\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1=mat(\"2 0;0 1\")\n",
    "B1=A1*B\n",
    "imprimir(A1,v,'=',A1*v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x937fa50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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llkSpAxKnlkSpoz4SpeZEqQMSp5ZEqQMCqCUhj7mLiEjDJOo7dxERaYC4hnui\n3AkngjoGm1mJma0KP56IUh2zzGyPma09wfyY3RkoglpitU06m9kiM1tvZuvM7IFaxiTUHZMSpa8j\nrEW9/d35fvS2cy4uD6q/z2MT0A1oAnwKnFdjzDDgXcCAHGBZnOoYDPwlBtvkcqAvsPYE86O+PepR\nS6y2SQegb/j5acDn8eiTgPspJvWqt0+6Fi96O57v3GN2J5wA6ogJ59yHwIHvGRKL7RFpLTHhnNvl\nnMsPPz8EfEb1DTOOF7PtEoFE6etIa4kJ9XatdUS1t+MZ7ie6y019x8SiDoCB4V+L3jWzXgHXEKlY\nbI/6iOk2MbMuQB9gWY1ZibRdEqWv67Me9fZ3NfrejumdmBqxfCDDOVdqZsOAeVTfNPlUFtNtYmat\ngLeAB51zB6O1nlOQevu7vOjteL5zD/ROONGswzl30DlXGn4+H0gxs9SA64hELLZHRGK5Tcwsherm\nf805N7eWIQmzXSKsJVb1qrdPgi+9Hc9wj9mdcBpah5m1NzMLP+9P9XbbH3AdkYjF9ohIrLZJeB0z\ngc+cc789wbCE2S4kTl9HVIt6+7t86e24HZZxMbwTTgB13ASMN7MKoAy4xYU/yg6Smc2h+pP6VDPb\nATwJpBxXR9S3Rz1qick2AQYBtwNrzGxVeNpjQMZxtcRsu9QlUfq6HrWotz3tbV2hKiLiIV2hKiLi\nIYW7iIiHFO4iIh5SuIuIeEjhLiLiIYW7iIiHFO4iIh5SuIuIeOj/A3ZlU+gPlqDIAAAAAElFTkSu\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa66e6f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mat2(B,B1,-0.1,-0.1,2.1,3.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\left[\\begin{matrix}1 & 0\\\\0 & 2\\end{matrix}\\right]$$\\left[\\begin{matrix}x\\\\y\\end{matrix}\\right]$$=$$\\left[\\begin{matrix}x\\\\2 y\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A2=mat(\"1 0;0 2\")\n",
    "B2=A2*B\n",
    "imprimir(A2,v,'=',A2*v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa6658b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KgUrn3G4P6xTxXKx6e8bkkXRNO/FbLSMtxIzJI0+l7ECYMXkkGS2uFkr2Y+K1SK6WuRi4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\nCaD/B4UIGAYCmRnGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa61dad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mat2(B,B2,-0.1,-0.1,2.1,3.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Intercambiar ejes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right]$$\\left[\\begin{matrix}x\\\\y\\end{matrix}\\right]$$=$$\\left[\\begin{matrix}y\\\\x\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A3=mat(\"0 1;1 0\")\n",
    "B3=A3*B\n",
    "imprimir(A3,v,'=',A3*v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa5f2ab0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xa725370>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mat2(B,B3,-0.1,-0.1,2.1,3.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Deslizar figuras"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\left[\\begin{matrix}1 & 0.5\\\\0 & 1\\end{matrix}\\right]$$\\left[\\begin{matrix}x\\\\y\\end{matrix}\\right]$$=$$\\left[\\begin{matrix}x + 0.5 y\\\\y\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A4=mat(\"1 0.5;0 1\")\n",
    "B4=A4*B\n",
    "imprimir(A4,v,'=',A4*v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa82cd70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+7r2oO00bxmpa47ptd14hry7cytX9O9FN88WeEIW7SMCemr2e1OYNuXmIRu3l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\nu4iIh/4H4B3QDoRa++gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa859330>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mat2(B,B4,-0.1,-0.1,2.1,3.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Rotar figuras"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]$$\\left[\\begin{matrix}x\\\\y\\end{matrix}\\right]$$=$$\\left[\\begin{matrix}\\frac{\\sqrt{2} x}{2} - \\frac{\\sqrt{2} y}{2}\\\\\\frac{\\sqrt{2} x}{2} + \\frac{\\sqrt{2} y}{2}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha=pi/4\n",
    "A5=Matrix([[cos(alpha) , -sin(alpha)],[sin(alpha), cos(alpha)]])\n",
    "B5=A5*B\n",
    "imprimir(A5,v,'=',A5*v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa602470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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CQUREAAWCiIh4FAgiIgIoEERExKNAEBERQIEgIiIeBYKIiAAKBBER8SgQREQE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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa8fc050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mat2(B,B5,-1.0,-1.5,1.0,1.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Proyectar sobre ejes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\left[\\begin{matrix}1 & 0\\\\0 & 0\\end{matrix}\\right]$$\\left[\\begin{matrix}x\\\\y\\end{matrix}\\right]$$=$$\\left[\\begin{matrix}x\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A6=mat(\"1 0;0 0\")\n",
    "B6=A6*B\n",
    "imprimir(A6,v,'=',A6*v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa602570>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HKMK9TtKYDq9HJ5Ydx90Xu3uJu5cUFhYes6673+aYrb/lMRM4JrGLpLeBOEQR7mskzU5c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\nHQACRLgDQIAIdwAI0P8BKuXyOElKRfoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa9845f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mat2(B,B6,-0.1,-0.1,2.1,3.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\left[\\begin{matrix}0 & 0\\\\0 & 1\\end{matrix}\\right]$$\\left[\\begin{matrix}x\\\\y\\end{matrix}\\right]$$=$$\\left[\\begin{matrix}0\\\\y\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A7=mat(\"0 0;0 1\")\n",
    "B7=A7*B\n",
    "imprimir(A7,v,'=',A7*v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0xaa591d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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OuRdI2t3m+Z74WLfMX7tDDe1OQTS79P1Xf9O76vqwde9+ctJYw/EmzV+7Iw3V9EuR9PaK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\nItwBIED/D0pL0YrJPEm2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xaa7dbf0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mat2(B,B7,-0.1,-0.1,2.1,3.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Transformación de $\\mathbb{R}^2$ en $\\mathbb{R}^3$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\left[\\begin{matrix}1 & 0\\\\1 & 0\\\\0 & 1\\end{matrix}\\right]$$\\left[\\begin{matrix}x\\\\y\\end{matrix}\\right]$$=$$\\left[\\begin{matrix}x\\\\x\\\\y\\end{matrix}\\right]$$, \\ \\ \\ \\ \\ $$\\left[\\begin{matrix}1 & 0\\\\1 & 0\\\\0 & 1\\end{matrix}\\right]$$\\left[\\begin{matrix}0 & 0 & 0.5 & 1 & 1 & 0\\\\0 & 1 & 1.5 & 1 & 0 & 0\\end{matrix}\\right]$$=$$\\left[\\begin{matrix}0 & 0 & 0.5 & 1 & 1 & 0\\\\0 & 0 & 0.5 & 1 & 1 & 0\\\\0 & 1 & 1.5 & 1 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A8=mat(\"1 0;1 0;0 1\")\n",
    "B8=A8*B\n",
    "imprimir(A8,v,'=',A8*v,', \\ \\ \\ \\ \\ ',A8,B,'=',A8*B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vX8eTTz6JN954I288Vy2w6wmZgCzZFxcXYbfbcfjwYczNzdXsppEiZOHookI3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\n8/Dw8EQJ/x/ERcqndl027AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa9addb0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import axes3d\n",
    "\n",
    "fig=plt.figure()\n",
    "ax=fig.gca(projection='3d')\n",
    "ax.plot(B8.T.col(0),B8.T.col(1),B8.T.col(2))\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}