Optimization and Computational Linear Algebra

Catalog description

This proof-based course covers the fundamentals of computational linear algebra and optimization used in Data Science. About two thirds of the lectures will be about linear algebra and the remaining third about convex optimization. We will first go over basic linear algebra: vector spaces, linear transformations, rank, norms and inner products, eigenvalues and eigenvectors, building up the singular value decomposition (SVD), which is a cornerstone of many numerical applications: PCA and dimensionality reduction, Markov chains and PageRank, spectral clustering in graphs, linear regression. Lastly, we will go over convex functions, optimality conditions in constrained optimization, and gradient descent.