{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Transformações Lineares\n", "#### Em Matemática, uma transformação linear é um tipo particular de função entre dois espaços vetoriais que preserva as operações de adição vetorial e multiplicação por escalar. Uma transformação linear também pode ser chamada de aplicação linear ou mapa linear." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Definição:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Se **T: V → W** é uma função de um espaço vetorial **V** em um outro espaço vetorial **W**, então **T** é chamada uma **transformação linear** de **V** em **W** se, para quaisquer vetor **u** e **v** em **V** e qualquer escalar **c** valem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- $a) T(u + v) = T(u) + T(v)$\n", "- $b) T(cv) = cT(v)$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "No caso especial em que **V = W**, a transformação linear é chamada um **operador linear** de **V**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Importação das Bibliotecas" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# importando a biblioteca numpy do python\n", "import numpy\n", "# importando a biblioteca matplotlib do python\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# importando a biblioteca 'plot_helper'\n", "from plot_helper import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Vetor Representado em Diferentes Pontos no Plano Cartesiano" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos agora começar a ver como podemos representar computacionalmente, no Python, vetores em um plano cartesiano." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# definindo um vetor qualquer\n", "vetor = [(2,2)] \n", "# pontos de origem do vetor acima\n", "origens = [(0,-1), (0,1), (0,0), (0,2)] \n", "# plota os gráficos do vetor, com seu respectivo módulo, direção, sentido e origem\n", "plot_vector(vetor, origens) \n", "# título do gráfico\n", "plt.title(\"Um vetor com diferentes pontos de origem.\"); " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Soma de Vetores" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos agora realizar a soma entre dois vetores, dado que teremos um vetor resultante dessa operação." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# soma de vetores\n", "\n", "# primeiro vetor\n", "vetorA = numpy.array((4,-2)) \n", "# segundo vetor\n", "vetorB = numpy.array((-2,6)) \n", "\n", "# uma lista de vetores = vetorA, vetorB e a soma vetorA + vetorB\n", "vetores = [vetorA, vetorB, vetorA + vetorB] \n", "\n", "# plota na tela o grafico dos vetores definidos\n", "plot_vector(vetores) \n", "# título do gráfico\n", "plt.title(\"Soma de dois vetores: (4,-2) + (-2,6) = (2,4)\"); " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Subtração de Vetores" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos agora realizar a subtração entre dois vetores, dado que teremos um vetor resultante dessa operação." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# subtração de vetores\n", "\n", "# primeiro vetor\n", "vetorA = numpy.array((4,-2)) \n", "# segundo vetor\n", "vetorB = numpy.array((-2,6)) \n", "\n", "# uma lista de vetores = vetorA, vetorB e a subtração vetorA - vetorB\n", "vetores = [vetorA, vetorB, vetorA - vetorB] \n", "\n", "# plota na tela o grafico dos vetores definidos\n", "plot_vector(vetores) \n", "# título do gráfico\n", "plt.title(\"Subtração de dois vetores: (4,-2) - (-2,6) = (6,-8)\"); " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Multiplicação de um Vetor por um Escalar" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos agora realizar a multiplicação de um vetor por um escalar, dado que teremos um vetor resultante dessa operação." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# multiplicação de um vetor por um escalar\n", "\n", "# criando um vetor c\n", "vetorC = numpy.array((1,1)) \n", "# definindo uma lista de vetores, em que o vetorC é multiplicado por escalares\n", "vetores = [vetorC, 2 * vetorC, -2 * vetorC] \n", "# plota o gráfico dos dois vetores na tela\n", "plot_vector(vetores) \n", "# título do gráfico\n", "plt.title(\"Multiplicação do vetor (1,1) por escalares 2 e -2\"); " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Base Canônica de um Vetor" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# bases de um vetor\n", "\n", "# definindo a componente i da base\n", "i = numpy.array((1,0)) \n", "# definindo a componente j da base\n", "j = numpy.array((0,1)) \n", "\n", "#definindo a liste de vetores\n", "vetores = [i, j]\n", "\n", "# plota o gráfico dos vetores definidos\n", "plot_vector(vetores) \n", "# título do gráfico\n", "plt.title(\"Base Canônica\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos mostrar que através da base canônica podemos representar qualquer vetor possível." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# definindo uma lista de vetores\n", "vetores = [i, j, (4 * i), (3 * j), (4 * i + 3 * j)] \n", "\n", "# plota o gráfico dos vetores definidos\n", "plot_vector(vetores) \n", "\n", "# título do gráfico\n", "plt.title(\"Combinações feitas com os vetores da base canônica, resultando no vetor (4,3)\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Conjunto de Todas as Combinações Lineares Possíveis Entre Dois Vetores" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# importa a função da biblioteca Python: randint\n", "from numpy.random import randint \n", "\n", "# conjunto de todas as combinações lineares possíveis entre dois vetores\n", "vetores = [] # lista vazia\n", "\n", "# definindo a componente i da base\n", "i = numpy.array((1,0)) \n", "# definindo a componente j da base\n", "j = numpy.array((0,1)) \n", "\n", "# estrutura de repetição for, 1000 vezes, para o conteúdo abaixo\n", "# nesse caso imprime 1000 vetores possíveis, resultado da combinação linear de outros dois vetores, \n", "# no intervalo de (0,0) até (-10,10)\n", "\n", "for _ in range(1000):\n", " # escolhe um número aleatório entre -10 e 10\n", " m = randint(-10,10) \n", " # escolhe um número aleatório entre -10 e 10\n", " n = randint(-10,10) \n", " # acrescenta a lista o vetor combinado com a base\n", " vetores.append(m * i + n * j) \n", "\n", "# a lista incialmente vazia, agora armazena 1000 vetores na mémoria da máquina\n", "\n", "# plota o gráfico da lista de vetores definidas\n", "plot_vector(vetores) \n", "# título do gráfico definido\n", "plt.title(\"1000 vetores aleatórios criados a partir da base canônica\"); " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### O mesmo pode ser feito a nível de combinação linear de dois vetores:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# primeiro vetor\n", "vetorA = numpy.array((2,-1)) \n", "# segundo vetor\n", "vetorB = numpy.array((-1,3)) \n", "\n", "# lista vazia\n", "vetores = [] \n", "\n", "#estrutura de repetição for que gera 10 vetores a partir de combinações aleatórias dos vetores a e b, \n", "# com escalares entre -10 e 10\n", "for _ in range(10):\n", " # escolhe um número aleatório entre -10 e 10\n", " escalar1 = randint(-10,10) \n", " # escolhe um número aleatório entre -10 e 10\n", " escalar2 = randint(-10,10) \n", " # acrescenta a lista o vetor combinado com a base\n", " vetores.append(escalar1 * vetorA + escalar2 * vetorB) \n", " \n", "# a lista incialmente vazia, agora armazena 10 vetores na mémoria da máquina\n", "\n", "# plota o gráfico da lista de vetores definidas\n", "plot_vector(vetores) \n", "\n", "# título do gráfico definido\n", "plt.title(\"10 combinações lineares entre o vetor (2,-1) e (-1,3), com escalares aleatórios\"); " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Podemos ter um vetor colinear, em que tendo 3 ou mais pontos, podemos traçar uma reta sobre ele" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# primeiro vetor\n", "vetorA = numpy.array((2,-1)) \n", "# segundo vetor: A * -2, para se colinear\n", "vetorD = numpy.array((-4,2)) \n", "\n", "vetores = [] # lista vazia\n", "\n", "# estrutura de repetição for que gera 10 vetores aleatórios,com multiplicação por escalares entre (-10,10)\n", "for _ in range(10):\n", " # escolhe um número aleatório entre -10 e 10\n", " escalar1 = randint(-10,10) \n", " # escolhe um número aleatório entre -10 e 10\n", " escalar2 = randint(-10,10) \n", " # adiciona a lista um vetor combinado da base\n", " vetores.append(escalar1 * vetorA + escalar2 * vetorD) \n", " \n", "# a lista incialmente vazia, agora armazena 10 vetores na mémoria da máq\n", "\n", "# plota o gráfico da lista de vetores definidos\n", "plot_vector(vetores) \n", "\n", "# título do gráfico\n", "plt.title(\"10 combinações lineares entre os vetores (2,-1) e -2(2,-1), com escalares aleatórios\"); " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Transformações Lineares" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos usar uma matriz de transformação linear\n", "$$\\begin{bmatrix}\n", " -2 & 1 \\\\\n", " 1 & -3 \\\\ \n", " \\end{bmatrix}$$\n", "a partir da base canônica." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# vamos fazer uma transformação linear\n", "# temos a base usual do plano cartesiano x * (1,0) + y * (0,1)\n", "\n", "# definimos uma matriz de transformação linear\n", "baseA = numpy.array([(-2,1),(1,-3)]) \n", "\n", "# agora temos uma nova base fruto da transformação linear\n", "plot_linear_transformation(baseA) \n", "# x * (-2,1) + y * (1,-3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Aplicando uma Transformação Linear em um Vetor" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos usar uma matriz de transformação linear" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\begin{bmatrix}\n", " 1 & 2 \\\\\n", " 2 & 1 \\\\ \n", " \\end{bmatrix}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "a partir da base canônica. Vamos usar o vetor (1,2)." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Aplicando uma Transformação Linear em um Vetor')" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# vamos fazer uma transformação linear (exemplo 1)\n", "# temos a base usual do plano cartesiano x * (1,0) + y * (0,1)\n", "\n", "# definimos uma matriz de transformação linear\n", "baseM = numpy.array([(1,2),(2,1)]) \n", "\n", "# definimos um vetor\n", "vetorX = numpy.array((1,2)) \n", "\n", "# definimos o vetor em duas situações: na base canônica e após a mudança de base\n", "vetores = [vetorX, baseM.dot(vetorX)] # lista de vetores\n", "# o segundo vetor da lista trata da multiplicação do vetorX pela nova matriz \n", "\n", "# plotar o gráfico da lista de vetores\n", "plot_vector(vetores) \n", "\n", "# título do gráfico\n", "plt.title(\"Aplicando uma Transformação Linear em um Vetor\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Observe que o vetor foi dilatado. Vamos usar um outro vetor para ver se a dilatação fica mais clara de se analisar." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Aplicando uma Transformação Linear em um Vetor')" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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mMhEREc9UJiIi4pnKREREPFOZiIiIZyoTERHxTGUiIiKeqUwkLhhjLjPGWPfPuYtIF1OZSMxz/4LqbL9ziCQylYnEg3tw/0dPEfGHykRimjHmDJw/6f2C31lEElm0/w94kagxxqTj/OdBJ+P8v+MdmcfBe5kkGTgA9/+1sO38T9tEEo3KRGLZTcBia22Z+/+Od8R/Ipg2Gyjt4HJE4lpc/dXg5557zqalpZGUFIyzdw0NDdTU1BCkTBAfuYqLi7n77rtZuHAhSUlJlJeXc95553HnnXcydOjQdi9z7Nix7Z52xYoVZGVl7X3CLhAP27ArBTnXuHHjjN85OkNcHZmkpqYyePBg0tPT/Y4CQHV1NYWFhYHKBPGRa926daSkpHD99dcDsGvXLgAefvhhevbsyT333MOAAQP2usyioqI2x5eXlzcVTk5ODjk5Oe15KlEXD9uwKwU5V7yIqzJJTk4mPT2dzMxMv6M0CWImiP1c8+bNY968eU3DJSUlHHbYYSxcuJAxY8a0e3m5ubltjs/IyGi6nZaWFqj1FevbsKsFNVe8CM7xnoiIxCyVicS8K6+8ksmTJ3/jtoh0nbg6zSWJ6a677vI7gkjC05GJiIh4pjIRERHPVCYiIuKZykRERDxTmYiIiGcqExER8UxlIiIinqlMRETEM5WJiIh4pjIRERHPVCYiIuKZykRERDxTmYiIiGcqExER8UxlIiIinqlMRETEM5WJiIh4pjIRERHPVCYiIuKZykRERDxTmYiIiGcqExER8UxlIiIinqlMRETEM5WJiIh4pjIRERHPUvwOINIRzzzzDEuXLmX37t3U1tZSW1vLr371K8455xy/o4kkJJWJxKT777+fKVOmMG3aNABWr17ND37wA4444giOOuoon9OJJB6d5pKYNH/+fKZMmdI0PGbMGBoaGvjwww99TCWSuHRkIjFpxIgRTbe/+uorFixYwODBgznppJMimk9paWmb48vKyjqUTyTRxFWZ1NfXU11d7XeMJtXV1YHLBPGV66qrrmLVqlXk5uby5JNPYq2lsrKy3Y/Pzs5u97Q1NTURzTua4mkbdoUg58rMzPQ7Rqcw1lq/M3Sa5557zqalpZGUFIyzdw0NDdTU1BCkTBB/uerr61m2bBlr165l0aJF9O7du92PHTt2bLunXbFiBVlZWe2ePpribRtG047KWorLdjKkb89A5QJnfY0bN874naMzxNWRSWpqKoMHDyY9Pd3vKIDzqaOwsDBQmSA+cx1zzDEMGTKEV155hXnz5rX7cUVFRW2OLy8vbyqcnJwccnJyIsoVLfG4DTtbRc0u7n5qPUvW/J01N81g187/BiJXqKAdKXkRV2WSnJxMenp6oA4bg5gJYj9XXV0d3bt3b3bft7/9bT788MOInlNubm6b4zMyMppup6WlBWp9xfo2jJbddV+x+NlXmPf4GrZ/WcXMiXkcPfBQCgq2B3J9xYu4KhNJHMOHD2fTpk3N7isrK+OEE07wKZH4raGhgd+/+CbXPvwMJeU7AEjr0Z3rpn3f52SJITgnD0UisHnzZtasWdM0/Pjjj/PBBx9wwQUX+JhK/GCt5YU3NzF8xjzO/+3DTUUC8ItJ4zmo97d8TJc4dGQiMenuu+9m/vz53HLLLdTX12OM4dlnn2XUqFF+R5Mu9P7WMn5+1+9Z//YH3xjXe990fnnuBB9SJSaVicSkyy67jMsuu8zvGOKzbx+cxfyf/IAF/7eWp//2drNx15z/fXpmpPmULPHoNJeIxKykpCR6Zabz+uaPmt1/aFZvfjYxz6dUiUllIiIx64Ot5Yy96nbKdnzJvuk9OOP4owGY95Mz2ad7N5/TJRad5hKRmBReJH/53ZXs0y2Fj8t3MuXEkX7HSzgqExGJOS0VyXGDD8day6Nzpgfqt9wThda4iMSU1ooEwBjDsJxDfE6YmFQmIhIz2ioS8ZfKRERigook2FQmIhJ4KpLgU5mISKCpSGKDykREAktFEjtUJiISSCqS2KIyEZHAUZHEHpWJiASKiiQ2qUxEJDBUJLFLZSIigaAiiW0qExHxnYok9qlMRMRXKpL4oDIREd+oSOKHykREfKEiiS8qExHpciqS+KMyEZEupSKJTyoTEekyKpL4pTIRkS6hIolvKhMRiToVSfxTmYhIVKlIEoPKRESiRkWSOFL8DiDSUStXruTBBx+kvr6eiooKDjnkEBYsWMDhh+vNKghUJIlFRyYSs6ZOncrs2bN58cUXeeONN8jMzOSUU05h165dfkdLeMWln6pIEozKRGLWmWeeyYQJEwBISkri0ksvpbi4mI0bN/qcLLFt3V7B96+5X0WSYHSaS2LWqlWrmg336NEDgLq6unbPo7S0tM3xZWVlkQdLYMWln3LVshfZUVWrIkkwcVUm9fX1VFdX+x2jSXV1deAyQfzmWr9+PQcddBBHH300lZWV7XpMdnZ2u+dfU1PT7vlGWxC3YXHpp5z2m/vYUVVLZuo+PHX9DI7MPiAQ6yyI6wucXJmZmX7H6BRxVSa1tbVs3ryZpKRgnL1raGgIXCaIz1x1dXX87ne/4+KLL+bdd9+NSr7i4mIqKiqiMu9IBW0bbt1e0XREktY9hd9OHk1y9XYKCrb7HQ0I3vpq1NDQQJ8+ffyO0SniqkxSU1MZPHgw6enpfkcBnE8dhYWFgcoE8Zlr5syZnHvuuVx11VURPa6oqKjN8eXl5YwdOxaAnJwccnJyIpp/tARpGxaXfsqv7rm/6Yhk/rmjmDThe77nChWk9RUqaEdKXsRVmSQnJ5Oenh6ow8YgZoL4yjVnzhxSU1NZsGABxpiIlpebm9vm+IyMjKbbaWlpgVpfQdiGH2wt5/RrF1O+s4J903vw1PUzSK7e7nuulgRhfcWz4BzviXTArbfeSklJCUuWLMEYQ0FBAQUFBX7HSggt/R7JyNxD/Y4lPomrIxNJLIsXL2b58uUsXbq06XLg5557jv79+zNixAif08W31n4hMQhftos/VCYSkyorK7nkkktoaGjg+OOPbzbukUce8SlVYtBvtktLVCYSkzIzM6mvr/c7RsJRkUhr9J2JiLSLikTaojIRkb1SkcjeqExEpE0qEmkPlYmItEpFIu2lMhGRFqlIJBIqExH5BhWJREplIiLNqEikI1QmItJERSIdpTIREUBFIt6oTERERSKeqUxEEpyKRDqDykQkgalIpLOoTEQSlIpEOpPKRCQBqUiks6lMRBKMikSiQWUikkBUJBItKhORBKEikWhSmYgkABWJRJvKRCTOqUikK6hMROKYikS6ispEJE6pSKQrqUxE4pCKRLqaykQkzqhIxA8qE5E4oiIRv6hMROKEikT8pDKRmFZXV8evf/1rUlJSKCkp8TuOb1Qk4jeVicSskpIS8vLy+OSTT6ivr/c7jm9UJBIEKhOJWVVVVSxfvpwf//jHfkfxTXHppyoSCQSVicSsIUOGMHDgQL9j+Gbr9gq+f839KhIJhBS/A4j4qbS0tM3xZWVlXZQkMsWln3LVshfZUVWrIpFAiKsyqa+vp7q62u8YTaqrqwOXCeIvV01NDeCc9qqsrIzosdnZ2REtJ9L5R0Nx6aec9ptF7KiqJTN1H566fgZHZh8QiGzxtm9FW3V1NZmZmX7H6BRxVSa1tbVs3ryZpKRgnL1raGgIXCaIv1xbtmwBYNOmTWzfvj1a8SguLqaioiJq82+Pjz/7ksse+SuVtXWkdU/ht5NHk1y9nYKC6D3vSMTbvhVtDQ0N9OnTx+8YnSKuyiQ1NZXBgweTnp7udxTA+dRRWFgYqEwQf7kaj0yGDBnCoYceGtEyi4qK2hxfXl7O2LFjAcjJySEnJyei+Xemp//xT2YseYG6PfX06J7CLVPymDThe3GxDaMtyLniRVyVSXJyMunp6YE6bAxiJoivXGlpaQBkZGRE/Hxyc3PbHJ+RkdFsOX6sry3/+S+X3/MH/vLWZgCSjGH1TTNJqdkZN9uwKwQ1V7yIqzIRiSdlO77gxsfWsGT1KzRY23T/bT+bxHePOIyCgp0+phNpTmUiMauuro4JEybwxRdfADB58mSys7NZtWqVz8m8qaiuZcH/reWOVX+lZldds3HDcrK5ctJ4qqqqfEon0jKVicSs7t27k5+f73eMTtXQ0MC9T6/n0Rde/UaRACz+xVSMMT4kE2lbcC5rEBGSkpL4zdTTWDJrKuGdMSlvOCOPOMyfYCJ7oTIRCZg/v7GJ0399LyFfk5CclMT8n5zlXyiRvVCZiASIUyT3NH3hvnT2+QzsdyAXnT6ab2dn+ZxOpHX6zkQkIFoqkp9+fzT//byCC089wed0Im1TmYgEQGtFAjDnvFNJTtZJBAk27aEiPmurSAAVicQE7aUiPtpbkYjECpWJiE9UJBJPVCYiPlCRSLxRmYh0MRWJxCOViUgXUpFIvFKZiHQRFYnEM5WJSBdQkUi8U5mIRJmKRBKBykQkilQkkihUJiJRoiKRRKIyEYkCFYkkGpWJSCdTkUgiUpmIdCIViSQqlYlIJ1GRSCJTmYh0AhWJJDqViYhHKhIRlYmIJyoSEYfKRKSDVCQiX1OZiHSAikSkOZWJSIRUJCLfpDKRmPb0009zzDHHMHr0aPLy8igsLIzq8lQkIi1L8TuASEe9+eabTJs2jQ0bNjBo0CAee+wxTj75ZIqKisjMzOz05f3tvWJm3v+cikSkBToykZh16623ctpppzFo0CAApk6dyp49e1i2bFlUlnfxnStUJCKtUJlIzHrxxRc59thjm4aTkpIYMWIE69ati8ryrIpEpFVxcZrLGJMC9Fm5ciXbtm0jIyPD70gAVFVV8dlnnwUqE8RHrs8//5wvv/yS7t27U1pa2nR/ZmYm//znP5vd15aysrI2x7/7/odfD+yu4daZZ3PKdw5r9/yjJR62YVcKcq4jjjjiYKDcWrvH7zxemMZPW7HMGHMw8B+/c4iIdFC2tdbfTygexctprj5+BxAR8SDm38Pi4jQX8BlAnz59WLZsGYcccojfefjss88455xzAAKTCeIr18iRI5k5cyYXXnhh030XX3wxKSkpLFq0qF3LLS8vb3P8li1buPjiiwF4/PHHGTFiRLvmG03xtA27QtBzufvgZ37n8SpeyqQenDeGQw45hNzcXL/zkJGR0fRGFZRMEF+5xo8fz9atW5umtdayZcsWrr766nY/r71Nl56e3nS7X79+gVhf8bQNu0Is5MJ9D4tl8XKaSxLQnDlzeP7559myZQsATzzxBMnJyVxwwQU+JxNJPPFyZCIJaOTIkSxbtowpU6aQmppKUlISf/nLX6LyC4si0jaVicS0s846i7POOsvvGCIJT6e5RETEM5WJiIh4pjIRERHPVCYiIuJZXHwB7/4ZApOfn2/79evndxwADj74YCoqKigoKCAomUC5InXQQQc13e7TJxi/pBzUdaVckWnMlZmZafzO0hl0ZCIiIp6pTERExDOViYiIeKYyERERz1QmIiLimcpEREQ8U5mIiIhnKhMREfEsrsukoaGBkSNH0r9/f7+jsHv3bq6//nry8vIYP348w4YN46yzzuKjjz7yLdPOnTuZO3cuo0aNYsyYMQwdOpR58+axZ88e3zKFKi4u5vjjj2fMmDG+Zfjzn//cdPv888+nsLDQtyyh6urqWLp0Kfvttx8lJSV+xwFg5cqVnHnmmVx11VXk5eVx9tln+7p/P/PMM5x++umcdNJJTJgwgRkzZvDUU0/5lqc1xpjLjDHWGDPG7yxexMVvwLdm0aJFFBcX07NnT7+j8Pnnn7N06VLefvttsrKyaGhoYPLkyZx77rm89dZbvmRau3Ytq1at4tVXX6Vnz5588sknDB8+nLq6Om688UZfMjVavnw59913H8nJyb5lePPNN7nyyiubhs8++2xOPvlkioqKfP0/U0pKSjjnnHPYb7/9qK8Pzn/QN3XqVFauXMm3vvUthg0bxhVXXMEpp5zCu+++S48ePbo8z/3338+UKVOYNm0alZWV3HPPPVx44YUMHz6co446qsvztKSsrAxgtt85OkPcHpls27aNhx56iBkzZvgdBYBevXqxZs0asrKyAEhKSmL06NFN/0ugX5lmzZrVVLZ9+/Zl0qRJrFixwrdMjXr37uZ18lcAAA9USURBVM3LL7/MwIEDfctw6623Mm7cuKbhiRMnsmfPHpYtW+ZbJoCqqiqWLFnCqaee6muOcGeeeSYnnngi4Ozfl156KcXFxWzcuNGXPPPnz2fKlClNw0OHDqWhoYEPP/zQlzwt+eUvfwlws985OkPclsnll1/OzTffTGpqqt9RAOjevTvDhg1rGt62bRvLli3jiiuu8C3ThAkTuPDCC5vd16NHD+rq6nxK9LXTTjuN7t27+5rhxRdf5Dvf+U7TcFJSEiNGjGDdunU+poIhQ4YwYMAAXzO0ZNWqVc2GG49G/NqfRowYQUqKc/Llq6++YsWKFeTm5nLSSSf5kifc6tWrG/O94HeWzhCXZdK4kYL2yQ2cEhkxYgQDBgzg5JNP9v10UrjXXnuNH/7wh37H8N2OHTv48ssvOfDAA5vd36dPH1+/B4glr732Gn379uWEE07wNccll1zC4YcfzsaNG3n66afJyMjwNQ9AdXU1V199NbfccovfUTpN3JVJVVUVv/nNb7jrrrv8jtKifv36UVBQwEcffcTatWu56KKL/I7U5KWXXmLr1q1cc801fkfxXU1NDcA3jo722WefpnHSut27d7NgwQIWLlxIt27dfM2yaNEiSkpKGD58OBMmTGj8nsJX1157LTNnzgzMX6LuDDFTJsaYue4VD63+fPDBB8ybN4+ZM2c2+9Ph0TR37lyMMS3+7LvvvowdO7bFc8Z9+/bl5ptv5sEHH+z0K4TaytSY64MPPmj2mG3btjFz5kyeeeaZqF2w0JFcfklLSwO+eYpm9+7dTeOkdVdccQWTJk3i7LPP9jsKAMnJyUyfPh1rLXfccYevWd5++23eeOMNZs6c6WuOzhZLV3PdBixua4KBAweW3Xvvvbz33ntN529LSkooLy9nzJgxDBw4kAcffLBTQ82ePbvVnaKqqop3332Xo48+uumqm9CrkwYNGgTA5s2bOfLII7skU2Oujz/+uGl4586dTJw4kfvuu4/hw4d3Wg6vufzUu3dvevbsyaefftrs/vLycg4//HCfUsWGJUuW0K1bN+bPn+9rjrq6umZHlklJSQwYMIDNmzf7mAqee+45amtrGTduXOP7QuMVL3cZY74AfmqtDc5VAu0UM2Vira0CqtqaJj8/n1dffbXZZZtz587l0UcfJT8/Pyq5MjIyWj0HW1lZSa9evUhJSWH58uVs376d2bO/vgqw8XC7b9++XZapMVdpaWnT7TPOOIPrrruO8ePHA86bQTSugoskVxCMGzeOd999t2nYWsvGjRu5+uqrfUwVbHfeeSfl5eU8/fTTGGMoKCgAnC/Du9rw4cPZtGlTs/vKy8sZPXp0l2cJde2113LttdcCzj6/7777Tgb+DVxprc33M5sXMXOaKx48/PDDbN++HYBdu3Zx0003MWTIEI499lhf8uzatYuJEydy3HHH0a9fPzZs2MCGDRt44IEHfMkTNHPmzOGll15qGl69ejXJyclccMEFPqYKrsWLF7NixQrOPvts3nnnHTZs2MDq1at57733fMmzefNm1qxZ0zT817/+leLiYm2/aLHWxs3P+vXrbUVFhbXW2rKyMpuXl2cPPfRQu88++9i8vDz7yCOP2K5UUVFhGzNt3brVXnrppXbYsGF29OjRdtiwYXbq1Kl269atXZopNNdtt91mgRZ//BC6vp555hmbl5dns7KybM+ePW1eXp598MEHuzzTkiVLmtbJMcccYzdt2tTlGcLt3r3bjho1yg4YMMAC9rvf/a6dNGmSr5kqKipsUlJSi/tSV7/uGi1cuND+z//8jx01apQdOXKkPfLII+3KlSt9ydKan/3sZxZ43V1X7wArbADeSzvyY6y1Xd1fUZOfn29HjBjh628nh6qsrKSgoIAgZQLlikRpaSnZ2dkAFBUVkZub63MiRxDXFShXpCorK/V/wIuIiDRSmUjMCsIfghQRh8pEYtLy5cuZNm0aSUnahUWCQK9EiUlB+EOQIvK1mPk9E5FQp512WqfMZ2+/1xKEP70hEgviqkzq6+uprq72O0aT6urqwGWC+Mr11VdfUV9fT2VlZYeW2XilVnvU1NR0eDmdLZ62YVcIcq4gXV3mRVyVSW1tLZs3bw7MefSGhobAZYL4yrVjx46myz6jrbi4mIqKiqgvpz3iaRt2hSDnipc/9hhXZZKamsrgwYNJT0/3OwrgfOooLCwMVCYIbq4bbriB22+/vc1p8vPzm/39sN69e1NdXd3hP9dRVFTU5vjy8nLGjh0LQE5ODjk5OR1aTmcL6jZUrsgE7UjJi7gqk+TkZNLT0wN12BjETBDMXLNmzeL444/n6KOPbvVveO2///5N/+ERQLdu3UhOTu7w89jbLyGG5khLSwvU+griNgTlSlRxVSYS2zIyMujVqxdZWVl6wYvEmOCcPBQRkZilMpGY9OyzzzJmzBheeOEF3nnnHcaMGcNDDz3kdyyRhKXTXBKTJk6cyMSJE/2OISIuHZmIiIhnKhMREfFMZSIiIp6pTERExDOViYiIeKYyERERz1QmIiLimcpEREQ8U5mIiIhnKhMREfFMZSIiIp6pTERExDOViYiIeKYyERERz1QmIiLimcpEREQ8U5mIiIhnKhMREfFMZSIiIp6pTERExDOViYiIeKYyERERz1QmIiLimcpEREQ8U5mIiIhnKhMREfEsxe8AIpHauXMnCxcuZN26daSkpPDFF18wadIk5syZQ0qKdmkRP+iVJzHn+eefZ9WqVbz66qv07NmTTz75hOHDh1NXV8eNN97odzyRhKTTXBJzevfuzaxZs+jZsycAffv2ZdKkSaxYscLnZCKJS0cmEnNOPfXUb9zXo0cP6urqIp5XaWlpm+PLysoinqdIIoqrMqmvr6e6utrvGE2qq6sDlwniM9ff//53zjzzTCorKyN6XHZ2drunrampiXj+0RKP2zCagpwrMzPT7xidIq7KpLa2ls2bN5OUFIyzdw0NDYHLBPGXa+PGjXz00Udcc801FBQURC1fcXExFRUVUZt/JOJtG0ZbkHP16dPH7xidIq7KJDU1lcGDB5Oenu53FMD51FFYWBioTBDcXDfccAO33357m9Pk5+czfPjwpuFPPvmE++67jyeffJKhQ4dGvMyioqI2x5eXlzN27FgAcnJyyMnJiXgZ0RDUbahckQnakZIXcVUmycnJpKenB+qwMYiZIJi5Zs2axfHHH8/RRx9NRkZGi9Psv//+TZf/7ty5kylTprB48WJGjx7doWXm5ua2OT40R1paWqDWVxC3IShXooqrMpHYlpGRQa9evcjKytrrC76yspIzzjiD6667jvHjxwOwZMkSZsyY0RVRRSRMcE4eirTTrl27mDhxIscddxz9+vVjw4YNbNiwgQceeMDvaCIJS0cmEnMeeugh8vPzyc/P54477vA7joigIxOJQZdccgnW2hZ/RMQfKhMREfFMZSIiIp6pTERExDOViYiIeKYyERERz1QmIiLimcpEREQ8U5mIiIhnKhMREfFMZSIiIp6pTERExDOViYiIeKYyERERz1QmIiLimcpEREQ8U5mIiIhnKhMREfFMZSIiIp6pTERExDOViYiIeKYyERERz1QmIiLimcpEREQ8U5mIiIhnKhMREfEsxe8AIpHavXs3v/3tb8nPz6dbt27s2LGD/v37c/vtt3P44Yf7HU8kIenIRGLO559/ztKlS1m5ciXr1q2joKCAbt26ce655/odTSRhqUwk5vTq1Ys1a9aQlZUFQFJSEqNHj2bLli0+JxNJXCoTiTndu3dn2LBhTcPbtm1j2bJlXHHFFT6mEkls+s5EYta2bduYOHEihYWFzJo1ixtvvDHieZSWlrY5vqysrKPxRBJKXJVJfX091dXVfsdoUl1dHbhMED+59t13X/Lz8ykrK2Py5Mls27aNe+65J6JlZmdnt3vampoaKisrI5p/tMTLNuwqQc6VmZnpd4xOEVdlUltby+bNm0lKCsbZu4aGhsBlguDmeuSRR3jsscfanGbx4sUMGjToG/f/6Ec/Yvbs2eTl5XHYYYdFJV9xcTEVFRVRmXekgroNlSsyDQ0N9OnTx+8YnSKuyiQ1NZXBgweTnp7udxTA+dRRWFgYqEwQ3FzZ2dmcfvrpDBo0iLS0tBan6d27N8YYAJKTk5vuz8rKYvbs2SQnJzNixIh2L7OoqKjN8eXl5YwdOxaAnJwccnJy2j3vaArqNlSuyATtSMmLuCqT5ORk0tPTA3XYGMRMENxcBxxwAIcddlibuR599FG2b9/O7Nmzm+5rPP00YMCAiJ5Tbm5um+MzMjKabqelpQVqfQV1GypXYgrO8Z5IBB5++GG2b98OwK5du7jpppsYMmQIxx57rM/JRBJTXB2ZSGI48cQTKSgoYMKECWRkZFBVVcWRRx7J888/T/fu3f2OJ5KQVCYSc7KzsyO+aktEokunuURExDOViYiIeKYyERERz1QmIiLimcpEREQ8U5mIiIhnKhMREfFMZSIiIp6pTERExDOViYiIeKYyERERz1QmIiLimcpEREQ8U5mIiIhnKhMREfFMZSIiIp6pTERExDOViYiIeKYyERERz1QmIiLimcpEREQ8U5mIiIhnKhMREfFMZSIiIp6pTERExDOViYiIeKYykZjW0NDAyJEj6d+/v99RRBKaykRi2qJFiyguLvY7hkjCU5lIzNq2bRsPPfQQM2bM8DuKSMJTmUjMuvzyy7n55ptJTU31O4pIwkvxO4BIR6xevZqUlBROPfVU3njjjQ7Pp7S0tM3xZWVlHZ63SCKJqzKpr6+nurra7xhNqqurA5cJYj9XVVUVc+bM4U9/+hOVlZXs3r0bay2VlZURLzM7O7vd09bU1HRoGdEQ69uwqwU5V2Zmpt8xOoWx1vqdQQQAY8xc4Pq9THYs8CPgQ2vtopDHTbfW9u/AMiN5AWRba9s+lBFJUCoTCQxjTAaQsZfJtgMFwJdAg3tff6AP8DpOyfw0gmUevJdJkoEDgHKg3Fq7p73zFkkkKhOJeV6OTESkc+hqLhER8UxlIjHLGNPHGJMPTAf6GGPyjTHTfQ0lkqB0mktERDzTkYmIiHimMhEREc9UJiIi4pnKREREPFOZiIiIZyoTERHxTGUiIiKeqUxERMQzlYmIiHimMhEREc9UJiIi4pnKREREPFOZiIiIZyoTERHxTGUiIiKeqUxERMQzlYmIiHimMhEREc9UJiIi4pnKREREPFOZiIiIZyoTERHx7P8DL5e/PeIJMmgAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# vamos fazer uma transformação linear (exemplo 2)\n", "# temos a base usual do plano cartesiano x * (1,0) + y * (0,1)\n", "\n", "# definimos uma matriz \n", "baseM = numpy.array([(1,2),(2,1)]) \n", "# definimos um vetor\n", "vetorX = numpy.array((1,1)) \n", "\n", "# definimos o vetor em duas situações: na base canônica e após a mudança de base\n", "\n", "# lista de vetores\n", "vetores = [vetorX, baseM.dot(vetorX)] \n", " # plotar o gráfico da lista de vetores\n", "plot_vector(vetores)\n", "\n", "# título do gráfico\n", "plt.title(\"Aplicando uma Transformação Linear em um Vetor\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Rotação\n", "Vamos definir uma matriz de transformação linear responsável por rotacionar os vetores, mudando os seus sentidos." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos usar uma matriz de transformação linear" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\begin{bmatrix}\n", " 0 & -1 \\\\\n", " 1 & 0 \\\\ \n", " \\end{bmatrix}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "a partir da base canônica. " ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "# definindo uma matriz de tranformação linear que rotaciona vetores\n", "rotacao = numpy.array([[0,-1], [1,0]]) " ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plotando o gráfico da transformação linear de rotação\n", "plot_linear_transformation(rotacao) " ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Aplicando uma Transformação Linear em um Vetor')" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# definimos um vetor\n", "vetorX = numpy.array((1,2)) \n", "\n", "# definimos o vetor em duas situações: na base canônica e após sofrer a rotação\n", "\n", "# lista de vetores\n", "vetores = [vetorX, rotacao.dot(vetorX)] \n", "# aplicando a rotação no vetorX\n", "\n", "# plotar o gráfico da lista de vetores\n", "plot_vector(vetores) \n", "\n", "# título do gráfico\n", "plt.title(\"Aplicando uma Transformação Linear em um Vetor\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mudança de escala\n", "Podemos também usar uma transformação linear responsável por contrair um eixo e expandir outro, por exemplo." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos usar uma matriz de transformação linear" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\begin{bmatrix}\n", " 2 & 0 \\\\\n", " 0 & \\frac{1}{2} \\\\ \n", " \\end{bmatrix}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "a partir da base canônica. " ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# matriz de transformação que dobra o eixo x e diminui pela metade o eixo y\n", "escala = numpy.array([[2,0], [0,0.5]]) \n", "\n", "# plotando o gráfico da nova base após a transformação linear\n", "plot_linear_transformation(escala) " ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Aplicando uma Transformação Linear em um Vetor')" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# definimos um vetor\n", "vetorX = numpy.array((1,1)) \n", "\n", "# definimos o vetor em duas situações: na base canônica e após a mudança de escala\n", "\n", "# lista de vetores\n", "vetores = [vetorX, escala.dot(vetorX)] \n", "# mundando a escala do vetor\n", "\n", "# plotar o gráfico da lista de vetores\n", "plot_vector(vetores) \n", "\n", "# título do gráfico\n", "plt.title(\"Aplicando uma Transformação Linear em um Vetor\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Aplicando Transformações Lineares Consecutivas" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "base = numpy.array([[0,1],[-1,0]]) # definindo uma matriz de transformação para a base canônica\n", "\n", "# a ordem de transformação é da direita para a esquerda\n", "plot_linear_transformations(rotacao, base) \n", "# plota os gráficos das duas transformações lineares na base de forma consecutiva" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Matriz Inversa" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Acima foi usado uma matriz de trasformação que, após a base ter sido transformada pela matriz de rotação, ela a trasnformou novamente para a base canônica. Vamos usar a ideia de matriz inversa para fazer o meso processo." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos usar uma matriz de transformação linear" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\begin{bmatrix}\n", " 1 & 2 \\\\\n", " 2 & 1 \\\\ \n", " \\end{bmatrix}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "a partir da base canônica. " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "# importando a função da biblioteca numpy, do conjunto de funções linalg: inv\n", "from numpy.linalg import inv " ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "baseM = numpy.array([(1,2),(2,1)]) # definimos uma matriz de transformação linear\n", "\n", "M_inversa = inv(baseM) # define uma matriz inversa \n", "\n", "# a ordem de transformação é da direita para a esquerda\n", "\n", "# plota os gráficos das duas transformações lineares na base de forma consecutiva\n", "plot_linear_transformations(baseM, M_inversa) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Funções definidas por L. Barba e T. Wang para uma apresentação no evento SciPy 2019:\n", "##### plot_vector, plot_linear_transformation e plot_linear_transformations¶" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Alguma Dúvida? Entre em Contato Comigo:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- [Me envie um e-mail](mailto:alysson.barbosa@ee.ufcg.edu.br);" ] } ], "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": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 4 }