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Land on Vector Spaces with Python

You learn to view matrices as linear transformations of vectors, and develop intuition about their role in linear systems of equations.

What You'll Learn

Making linear combinations of vectors, and the concepts of basis vectors and span
Matrix-vector multiplication as a combination of the matrix columns scaled by the vector coordinates
Setting up special transformation like rotation, shear, scaling, identity
What is special about eigenvectors: they stay on their span after transformation
Using functions from the NumPy Linalg library to compute vector norms, solve linear systems, find eigenvalues
Applications of eigenvectors in ecology, Markov Chains, Google's PageRank algorithm
Computing singular value decomposition and applying it to image compression, least squares problems, and linear regression