{"nbformat": 3, "metadata": {"signature": "sha256:ae14d4fed9cb3eea47f84acf30b6c66f2b6197ee976dfa82b001efd14a844f09", "name": ""}, "worksheets": [{"cells": [{"source": ["# Behavior of Elimination Matrices"], "metadata": {}, "cell_type": "markdown"}, {"cell_type": "code", "outputs": [], "prompt_number": 3, "input": ["import numpy as np"], "collapsed": false, "language": "python", "metadata": {}}, {"cell_type": "code", "outputs": [], "prompt_number": 30, "input": ["n = 4"], "collapsed": false, "language": "python", "metadata": {}}, {"source": ["----------------\n", "Let's create some elimination matrices:"], "metadata": {}, "cell_type": "markdown"}, {"cell_type": "code", "outputs": [{"text": ["array([[ 1. ,  0. ,  0. ,  0. ],\n", "       [ 0.5,  1. ,  0. ,  0. ],\n", "       [ 0. ,  0. ,  1. ,  0. ],\n", "       [ 0. ,  0. ,  0. ,  1. ]])"], "prompt_number": 40, "metadata": {}, "output_type": "pyout"}], "prompt_number": 40, "input": ["M1 = np.eye(n)\n", "M1[1,0] = 0.5\n", "M1"], "collapsed": false, "language": "python", "metadata": {}}, {"cell_type": "code", "outputs": [{"text": ["array([[ 1.,  0.,  0.,  0.],\n", "       [ 0.,  1.,  0.,  0.],\n", "       [ 0.,  0.,  1.,  0.],\n", "       [ 4.,  0.,  0.,  1.]])"], "prompt_number": 41, "metadata": {}, "output_type": "pyout"}], "prompt_number": 41, "input": ["M2 = np.eye(n)\n", "M2[3,0] = 4\n", "M2"], "collapsed": false, "language": "python", "metadata": {}}, {"cell_type": "code", "outputs": [{"text": ["array([[ 1. ,  0. ,  0. ,  0. ],\n", "       [ 0. ,  1. ,  0. ,  0. ],\n", "       [ 0. ,  1.3,  1. ,  0. ],\n", "       [ 0. ,  0. ,  0. ,  1. ]])"], "prompt_number": 42, "metadata": {}, "output_type": "pyout"}], "prompt_number": 42, "input": ["M3 = np.eye(n)\n", "M3[2,1] = 1.3\n", "M3"], "collapsed": false, "language": "python", "metadata": {}}, {"source": ["-------------------\n", "Now play around with them:"], "metadata": {}, "cell_type": "markdown"}, {"cell_type": "code", "outputs": [{"text": ["array([[ 1. ,  0. ,  0. ,  0. ],\n", "       [ 0.5,  1. ,  0. ,  0. ],\n", "       [ 0. ,  0. ,  1. ,  0. ],\n", "       [ 4. ,  0. ,  0. ,  1. ]])"], "prompt_number": 43, "metadata": {}, "output_type": "pyout"}], "prompt_number": 43, "input": ["M1.dot(M2)"], "collapsed": false, "language": "python", "metadata": {}}, {"cell_type": "code", "outputs": [{"text": ["array([[ 1. ,  0. ,  0. ,  0. ],\n", "       [ 0.5,  1. ,  0. ,  0. ],\n", "       [ 0. ,  0. ,  1. ,  0. ],\n", "       [ 4. ,  0. ,  0. ,  1. ]])"], "prompt_number": 44, "metadata": {}, "output_type": "pyout"}], "prompt_number": 44, "input": ["M2.dot(M1)"], "collapsed": false, "language": "python", "metadata": {}}, {"cell_type": "code", "outputs": [{"text": ["array([[ 1. ,  0. ,  0. ,  0. ],\n", "       [ 0.5,  1. ,  0. ,  0. ],\n", "       [ 0. ,  1.3,  1. ,  0. ],\n", "       [ 4. ,  0. ,  0. ,  1. ]])"], "prompt_number": 45, "metadata": {}, "output_type": "pyout"}], "prompt_number": 45, "input": ["M1.dot(M2).dot(M3)"], "collapsed": false, "language": "python", "metadata": {}}, {"source": ["BUT:"], "metadata": {}, "cell_type": "markdown"}, {"cell_type": "code", "outputs": [{"text": ["array([[ 1.  ,  0.  ,  0.  ,  0.  ],\n", "       [ 0.5 ,  1.  ,  0.  ,  0.  ],\n", "       [ 0.65,  1.3 ,  1.  ,  0.  ],\n", "       [ 4.  ,  0.  ,  0.  ,  1.  ]])"], "prompt_number": 47, "metadata": {}, "output_type": "pyout"}], "prompt_number": 47, "input": ["M3.dot(M1).dot(M2)"], "collapsed": false, "language": "python", "metadata": {}}], "metadata": {}}], "nbformat_minor": 0}