Advanced Linear Algebra

3 credits · Undergraduate

Orthogonal bases, orthogonal projections, Gram-Schmidt orthogonalization, Householder transformations, and Courant-Fisher min-max Theorem. Normal, self-adjoint matrices, pseudo inverses, and positive definite and semi-definite matrices. Matrix decompositions including QR factorization, diagonalization, Jordan decomposition, and singular value decomposition. Hilbert spaces, linear functionals, and Riesz Representation Theorem. Applications include least squares problems, regression models, optimization, data denoising, principle component analysis, and dimension reduction for data analysis. Prerequisite: 2501, 2600, or all of 2100, 2300, and 2410. [3] (MNS)