linear-algebra.md

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Imports

The tutorial below imports NumPy, Pandas, and SciPy.

importplotly.plotlyaspyimportplotly.graph_objsasgofromplotly.toolsimportFigureFactoryasFFimportnumpyasnpimportpandasaspdimportscipy

Add Two Matrices

A Matrix is a 2D array that stores real or complex numbers. A Real Matrix is one such that all its elements $r$ belong to $\mathbb{R}$. Likewise, a Complex Matrix has entries $c$ in $\mathbb{C}$.

matrix1=np.matrix( [[0, 4], [2, 0]] ) matrix2=np.matrix( [[-1, 2], [1, -2]] ) matrix_sum=matrix1+matrix2colorscale= [[0, '#EAEFC4'], [1, '#9BDF46']] font=['#000000', '#000000'] table=FF.create_annotated_heatmap(matrix_sum.tolist(), colorscale=colorscale, font_colors=font) py.iplot(table, filename='matrix-sum')

Multiply Two Matrices

How to find the product of two matrices

matrix1=np.matrix( [[1, 4], [2, 0]] ) matrix2=np.matrix( [[-1, 2], [1, -2]] ) matrix_prod=matrix1*matrix2colorscale= [[0, '#F1FFD9'], [1, '#8BDBF5']] font=['#000000', '#000000'] table=FF.create_annotated_heatmap(matrix_prod.tolist(), colorscale=colorscale, font_colors=font) py.iplot(table, filename='matrix-prod')

Solve Matrix Equation

How to find the solution of $AX=B$

A=np.matrix( [[1, 4], [2, 0]] ) B=np.matrix( [[-1, 2], [1, -2]] ) X=np.linalg.solve(A, B) colorscale= [[0, '#497285'], [1, '#DFEBED']] font=['#000000', '#000000'] table=FF.create_annotated_heatmap(X.tolist(), colorscale=colorscale, font_colors=font) py.iplot(table, filename='matrix-eq')

Find the Determinant

matrix=np.matrix( [[1, 4], [2, 0]] ) det=np.linalg.det(matrix) det

Find the Inverse

matrix=np.matrix( [[1, 4], [2, 0]] ) inverse=np.linalg.inv(matrix) colorscale= [[0, '#F1FAFB'], [1, '#A0E4F1']] font=['#000000', '#000000'] table=FF.create_annotated_heatmap(inverse.tolist(), colorscale=colorscale, font_colors=font) py.iplot(table, filename='inverse')

Find Eigenvalues

matrix=np.matrix( [[1, 4], [2, 0]] ) eigvals=np.linalg.eigvals(matrix) print("The eignevalues are %f and %f") %(eigvals[0], eigvals[1])

Find SVD

How to find the Singular Value Decomposition of a matrix, i.e. break up a matrix into the product of three matrices: $U$, $\Sigma$, $V^*$

matrix=np.matrix( [[1, 4], [2, 0]] ) svd=np.linalg.svd(matrix) u=svd[0] sigma=svd[1] v=svd[2] u=u.tolist() sigma=sigma.tolist() v=v.tolist() colorscale= [[0, '#111111'],[1, '#222222']] font=['#ffffff', '#ffffff'] matrix_prod= [ ['$U$', '', '$\Sigma$', '$V^*$', ''], [u[0][0], u[0][1], sigma[0], v[0][0], v[0][1]], [u[1][0], u[1][1], sigma[1], v[1][0], v[1][1]] ] table=FF.create_table(matrix_prod) py.iplot(table, filename='svd')

fromIPython.displayimportdisplay, HTMLdisplay(HTML('<link href="//fonts.googleapis.com/css?family=Open+Sans:600,400,300,200|Inconsolata|Ubuntu+Mono:400,700" rel="stylesheet" type="text/css" />')) display(HTML('<link rel="stylesheet" type="text/css" href="http://help.plot.ly/documentation/all_static/css/ipython-notebook-custom.css">')) ! pipinstallgit+https://github.com/plotly/publisher.git--upgradeimportpublisherpublisher.publish( 'python_Linear_Algebra.ipynb', 'python/linear-algebra/', 'Linear Algebra | plotly', 'Learn how to perform several operations on matrices including inverse, eigenvalues, and determinents', title='Linear Algebra in Python. | plotly', name='Linear Algebra', language='python', page_type='example_index', has_thumbnail='false', display_as='mathematics', order=10, ipynb='~notebook_demo/104')