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165/3Y2JiiImJ8SM0A9oucNYsJfjdu2HPHtWyX7lS+8RWrqwpfU2aQIECbkdr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\nRK5CYII=\n"}], "language": "python", "input": ["pt.plot(stickman[0], stickman[1])"], "collapsed": false}, {"metadata": {}, "source": ["Now define A to be a rotation matrix: (Use geometric intuition!)"], "cell_type": "markdown"}, {"prompt_number": 18, "metadata": {}, "cell_type": "code", "outputs": [], "language": "python", "input": ["alpha = 0.1*np.pi"], "collapsed": false}, {"prompt_number": 19, "metadata": {}, "cell_type": "code", "outputs": [], "language": "python", "input": ["A = np.array([\n", "    [np.cos(alpha), np.sin(alpha)],\n", "    [-np.sin(alpha), np.cos(alpha)]\n", "])"], "collapsed": false}, {"metadata": {}, "source": ["Now multiply the geometry by this matrix, reassign to `stickman`, and plot:"], "cell_type": "markdown"}, {"prompt_number": 39, "metadata": {}, "cell_type": "code", "outputs": [{"prompt_number": 39, "metadata": {}, "output_type": "pyout", "text": ["[<matplotlib.lines.Line2D at 0x7f894f882208>]"]}, {"metadata": {}, "text": ["<matplotlib.figure.Figure at 0x7f894f959e48>"], "output_type": "display_data", "png": 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WqdXxi96UKRrf/+mnoSsA4y7WuWsSRk4OvPmmyhDvvGNJv7h06qQ5EFddBUuW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\n8v+0h8qiKx7ZtgAAAABJRU5ErkJggg==\n"}], "language": "python", "input": ["stickman = np.einsum(\"ij,jk->ik\", A, stickman)\n", "pt.plot(stickman[0], stickman[1])"], "collapsed": false}, {"metadata": {}, "cell_type": "code", "outputs": [], "language": "python", "input": [], "collapsed": false}]}], "nbformat_minor": 0, "nbformat": 3}