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bFMEa9Y86ytp+mjQJO5rkUFBgCSHSGy56a9vWSpthfKZycnLIycn58f7DDz8c\nSgNyV+Ap7At9XdT+esCnQD9VHbrXcyYCdwCTgBGkaQOyK3+7d8NHH9mcUGvW2MJDLVuGHVXiuPJK\n+MUvUrv3VDoKa26iZ4HawFgRmSoiA4P9twFHAf2C/VNFJLIAXB9gEDAfWFBcInAuFoWFVhV07LHW\nVfSmm6xx0hPBnrp2hVdeObDxGC61+aAzl1LuuQfGjoWnn7Z1qV3xCgvhZz+zHlXXXRd2NC5eQu9a\nGm+eDNyBmjsX/vQnaxieNCl1p5aIp6+/trEu48fbMo0u+fkU1i5tbd4MTz4Jp50GnTrBtGmeCPZX\nx462+NLAgft+rEt9ngxcUlq0yBo/jzjCJlX77DOrIqpdO+zIksttt1nX5jfeCDsSF7YEnSjAuZKN\nGWNXtH36WH/ypk3Djih5HXEEjB5tc2UBXHttqOG4EHkycEnlwQfhtdfg3/9Ov9HD5aV1a5vE7txz\nbbRt165hR+TC4A3ILmmMG2dTd0ybZqOwXXxNmGDzFr39to1BcMnHG5BdSsvPtz7xPXrYZGCeCMrH\naadZiatnT5gzJ+xoXEXzZOASVn4+vPSSLZjy+uvw8cd+xVrezjoLHnvM5m96p7ipJ13K8jYDl5CW\nLYNLLrHJ9d56y76cXMXo1ctWRYtMZLc/K6O55OclA5dwXnrJplru2RM++cQTQRiOO85m1P3DH6xU\n5lKfNyC7hDJmjE2PMGGCzazpwjVnjq2ONnWqTYnuEps3ILuU8N13cM018J//eCJIFMceC7fealtB\nQdjRuPLkycAlhBkz4Je/LJpawiWOhx6yFfSGDw87EleePBm4UOXl2cIgXbrAvfda46VLLNWqwQMP\n2P+nuOVWXWrwZOBCs3KldWVctszqpm+8MeyIXEkuu8yWeRwyJOxIXHnxZOBCMWIEnHQSnHeefcHU\nrx92RG5ffvtbeOGFsKNw5aXMyUBE+ovIdyIyXUSGiEjdvY63EJGtInJ31L4OIjJTROaLyD9iCdwl\nr2XLoHdvm/bgoYegkl+SJIWLL4aFC62h36WeWE7DMUBbVT0emAfcv9fxAdg6x9FeAHqraiaQGayj\n7NLMLbfYVaavRJZcqla1wWiTJ4cdiSsPZU4GqjpWVSMrqE4EmkWOiUg3YBEwO2pfU6COqk4Kdr0B\ndCvr+7vk9OqrdnX5hz+EHYkrixtusLWlXeqJVwH9BmAkgIjUBv4IZO/1mAxgedT93GCfSxPvvQd9\n+8LQoVCoOTDqAAAVyklEQVSjRtjRuLLo0gVWrLDRyS61lDo3kYiMBQ4t5tADqjoseExfIE9V3w6O\nZQNPq+p2ESnTSDiA7OzsH29nZWWR5ZPXJ7VVq+Dmm+HTT23+fJecata0kkF2tk8amAhycnLIycmJ\ny2vFNB2FiPQCbgTOUdWdwb7PgObBQ+oBhcCDwBBgvKq2Dh7XAzhTVW8p5nV9OooU8/jjMH8+vPxy\n2JG4WC1eDKecAsuXWzuCSxyxTEdR5mQQNP4+hX2hryvhMf2ALao6ILg/EbgDmIQ1Lj+jqqOKeZ4n\ngxSycqVNPDdmDBx/fNjRuHi46CKbzO7xx8OOxEULa26iZ4HawFgRmSoiA/fjOX2AQcB8YEFxicCl\nlsJCG1V8yy2eCFLJyy/Dhx/6ILRU4rOWunL11FPwwQfw2WdQxVfPSCnvvgv/+pctR+oSQyjVROXJ\nk0FqGDcOrr4avvoKjjgi7GhcvG3YYP/XTZug7F1FXDz5FNYu4SxZYongnXc8EaSqBg1sPepJk/b9\nWJf4PBm4uMvPh6uugnvu8VHGqe7BB200ua91kPw8Gbi4++tfoXZtuOuusCNx5e36660tyBuSk5+3\nGbi4Wr8eMjNh+nRo3nzfj3fJb8QI+P3vYeZMW/vAhcfbDFxC2LwZunWzq0VPBOnjwgttfeSnnw47\nEhcLLxm4uNi9274UjjgC/vlPn5Y63SxbBu3awaJF1qjswuElAxeq1attrvuqVWHgQE8E6ahFC+ja\n1XqPueTkJQMXk7w8yMqCn/3MpibwuWrS1+TJVjqcM8dXrguLlwxcKObMsSTQsCE88YQngnR38snQ\nuTOM8klmkpInA1cmK1faFMa/+Q38978+1YQzPXr4OsnJypOBO2ALFkCnTtCnD9x6q09F4Ip0726N\nyRMnhh2JO1CeDNwBmTbNGovvuAMeeCDsaFyiqVLFlsZ8992wI3EHypOB2y87dlgDcZcucP/9voax\nK9kll8BHH4H3AUkungxcqfLybHRpixbwxRfWY6RnT68aciVr397WsZg2LexI3IHwZj9XooICuPRS\nGzcwaRK0bBl2RC4ZiMDvfgd//COMHRt2NG5/lblkICL9ReQ7EZkuIkNEpG7UsfYi8qWIzBKRGSJS\nLdjfQURmish8EflHPH4BV37+9jf44QebhCxdEsHkyXD66XD22bYgjyub226zaczHjw87Ere/Yqkm\nGgO0VdXjgXnA/QAiUgV4E7hJVY8DzgTyg+e8APRW1UwgM1hH2SWYLVtsfqFBg6whMB3GD6jCiy/C\nBRfATTdZI+i111obyaZNYUeXfKpUgYcess3bDpJDmZOBqo5V1cLg7kSgWXD7XGCGqs4MHrdRVQtF\npClQR1UjS2G8AXQr6/u78jFjBnTsaCfz1KnpMeFcfj7ceCM89xxMmGBtItdcA/PnW4nouuv8C60s\nevSw1dA+/DDsSNz+iFcD8g3AyOB2K0BFZJSITBGRe4L9GcDyqOfkBvtcAigogHvvhXPPhbvvtrVt\na9cOO6ryt3MnXH455Oba8pytWhUdq1rVEsScOTB6dHgxJqsqVWwm0wcf9GSaDEptQBaRscChxRx6\nQFWHBY/pC+Sp6ttRr3kacDKwAxgnIlOAAypsZ2dn/3g7KyuLrKysA3m6OwDffw+9etkJ++236TPr\n5Lx5Vgpo2RLee6/4ufirVYPHHrOFek45BerVq/g4k1mXLtagPH68tcO4+MrJySEnJycurxXTRHUi\n0gu4EThHVXcG+64AzlfVXsH9PwE7gcHAeFVtHezvAZypqrcU87o+UV0FKSy0L7lzz4Xs7PSZVuKl\nl2zQXHa2LdtYWldZVRtkN2uWzbtz0EEVFmZKePFFGDnSxh648hXKRHVB4+89wCWRRBAYDbQTkRpB\nY/KZwLequgrYLCKdRUSAnsDQsr6/i11+vvX6qF4dHn44fRLBX/8KAwbA55/b77+vMRMi8Pe/Wynh\n1VcrJsZU0rOnjVFZuDDsSFxpYmkzeBaoDYwVkakiMhBAVX8ABgBfA1OBKar6cfCcPsAgYD6wQFV9\nfsMQ/eY3VlUybBhUrhx2NBXj6afhtdes2qJ16/1/XuXK0Lu3TcrnDkzNmva3GzAg7EhcaXw9gzT1\n2GPw9tvWaFqrVtjRVIzPP7eJ1L7+umy9pDZvtvaFyZPTZ9xFvKxdC8ceC1Om2Gp4rnz4egbugIwc\naXXmo0enTyLYutWqKwYNKnt32YMPhjvvtLmZ3IFp3NjaZh5+OOxIXEm8ZJBm1q2zBUgGDLAJxdLF\nAw/Y1MqDB8f2Olu32iIu995rA/Pc/tu0CTIzbWT3sceGHU1qiqVk4MkgjeTl2YI0p51mjajp4vXX\n7Wp+8mQ47LDYX2/2bFvq8913vbvkgXr8cfjmG+vK6+LPk4HbJ1VrxNu4ET74IH0WrX/pJfjLX2zC\ntHhejX76qbU/fPgh/Pzn8XvdVLdtm5UORoyAE08MO5rU48nAlUoVbr7ZGk4//zw9RhaDjR7u3x/G\njYOjj47/648ebYP1Jk60Kb7d/nn2WfvbDR8ediSpxxuQXan697d+3umSCPLz4dFHrV3k00/LJxEA\nnHeerfVw2WU2rYXbPzfdBDNn2mfSJQ5PBinutddsoNSoUemRCD79FI47Dj75xG6XdzfGP/wBjjzS\n1oL2wuz+Oegg6NfPGvX9b5Y4vJooha1YYfXZgwbBOeeEHU3527TJ2gUGDoRu3SpuNbZt22xKj1tv\nhT59KuY9k11+PrRta1V5XbqEHU3q8DYD9xMrV1rPoauvTo+F63fvtmmnDz7YZlytaAsWwKmn2vw7\nP/tZxb9/Mnr3XavKmzjRl1GNF28zcHtYu9a6j6ZLItixw5bn3LYN/hHS+nlHH23zF911l1d97K9f\n/xp27fIJ7BKFlwxSTGGhNdAddBA8/3zY0ZS/ggL41a+gRg14881wV2UrKIB27azB/sILw4sjmYwa\nZZMFzpplEya62HjJwP3o0UdttbJ0GPavatNDbN0Kb7wR/vKclStbtcdvf2tLh7p969rVGvyfeirs\nSJyXDFKIKjRoYOMJyqs7ZSIZNMiqhSZMgLp1w46myA03WGIIo+0iGS1ebFN8fPcdHHJI2NEkNy8Z\nOMAa4g45BI46KuxIyt/Wrbac4htvJFYiAGs7+Owzi83tW8uWtvRoOlRrJjIvGaSIwkKre929Oz2u\nSP/8Z1ub+O239/3YMEyfbr25li/3ldH2x7x51ulh8eL0mUm3PHjXUsef/gRjxliDXIMGYUdTvhYv\nho4drSSUyKWgs8+27q433BB2JMmhRw84/HCbzM6VTSjJQET6AxcBecBC4HpV3SQi1YFXgbZAFeAN\nVX08eE4H4DWgOjBSVe8s4bU9GRyAjRutjeCbb+xkSmX5+XD66TZJ3O9/H3Y0pZs2zdaWHjrUxiC4\n0q1ZA8cfD0OG+FiNsgqrzWAM0FZVjwfmAZElP64EUNX2QAfgZhGJTOP1AtBbVTOBzGAdZRejYcPs\nCzLVEwFY9VDduvC734Udyb6dcIK1G3TrZvNCudIdcoi1G1x3nU237ipWmZOBqo5V1cLg7kSgWXB7\nJVBLRCoDtbCSw2YRaQrUUdV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"metadata": {}}], "collapsed": false, "language": "python", "input": ["pt.plot(stickman[0], stickman[1])"], "cell_type": "code", "prompt_number": 3, "metadata": {}}, {"cell_type": "markdown", "source": ["Now define A to be a rotation matrix:"], "metadata": {}}, {"outputs": [], "collapsed": false, "language": "python", "input": ["alpha = 0.1*np.pi"], "cell_type": "code", "prompt_number": 4, "metadata": {}}, {"outputs": [], "collapsed": false, "language": "python", "input": ["A = np.array([\n", "    [np.cos(alpha), np.sin(alpha)],\n", "    [-np.sin(alpha), np.cos(alpha)]\n", "])"], "cell_type": "code", "prompt_number": 5, "metadata": {}}, {"cell_type": "markdown", "source": ["Why does this matrix act as a rotation?\n", "\n", "* Think: What happens to $(1,0)^T$ and $(0,1)^T$ when they're multiplied by `A`?"], "metadata": {}}, {"cell_type": "markdown", "source": ["-------------------------\n", "\n", "Now multiply the geometry by this matrix, reassign to `stickman`, and plot:\n", "\n", "(Also try to evaluate this cell multiple times with Ctrl+Enter)"], "metadata": {}}, {"outputs": [{"text": ["[<matplotlib.lines.Line2D at 0x7f568d0fca58>]"], "output_type": "pyout", "prompt_number": 29, "metadata": {}}, {"text": ["<matplotlib.figure.Figure at 0x7f568d143748>"], "output_type": "display_data", "png": 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1wJgzBxYtMiVSujRMnw5HHAF161qfh0aNrFVjo0b2qF/fjnOcZOCYY0whzJiR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\nHAeA/we1X7PvQxtVWAAAAABJRU5ErkJggg==\n", "metadata": {}}], "collapsed": false, "language": "python", "input": ["stickman = A.dot(stickman)\n", "pt.plot(stickman[0], stickman[1])"], "cell_type": "code", "prompt_number": 29, "metadata": {}}, {"cell_type": "markdown", "source": ["* Observe that this is, nominally, matrix-matrix multiplication. (`stickman` is a 2D array)\n", "* However, `stickman` is really more 'array of vertices' than 'matrix'.\n", "* The math doesn't care either way though."], "metadata": {}}], "metadata": {}}], "nbformat_minor": 0, "metadata": {"signature": "sha256:a8b7c45ee837fd6e0da078ca8684e815042579264ec2993e0b7e7b018d1452e3", "name": ""}}