Land on Vector Spaces with Python

This is the fourth module in Engineering Computations (EngComp4), applying Python and core numerical libraries (NumPy, SymPy, Matplotlib) to explore the foundations of linear algebra, with a geometrical and practical approach. You learn to view matrices as linear transformations of vectors, and develop intuition about their role in linear systems of equations. Playing with transformations, you understand eigenvalues and eigenvectors, and discover matrix decomposition. We use Python to compute all the eigenthings and apply them to population models in ecology, Markov Chains, and the Google Page Rank algorithm. You learn about singular-value decomposition and its application to image compression, least squares problems, and linear regression. The target audience is second-year science and engineering students, with minimal background in linear algebra through a first college course or even high-school mathematics.