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Course Description

Summary

This is a second course on linear algebra. The primary focus will be on matrix decompositions (especially spectral, singular value, and QR decompositions), related concepts (e.g. Moore-Penrose psuedoinverse), and their applications. Applications will include least squares, principal component analysis, google search, data compression, and discrete and fast Fourier transforms. There will also be a secondary focus on representation theory and the geometry of Lie groups, with applications to geometry and physics. In addition, there will be an introduction to tensors and their applications. However, the class will not have a focus on proofs. The class should be of interest for both theoretical and applied reasons. The course will be particularly important for statistics and for computer science (especially machine learning). Students will have a choice on assignments, whether to pursue a theoretical or an applied emphasis (or some mix of both).