MATH 318 A: Advanced Linear Algebra Tools and Applications

Eigenvalues, eigenvectors, and diagonalization of matrices: nonnegative, symmetric, and positive semidefinite matrices. Orthogonality, singular value decomposition, complex matrices, infinite dimensional vector spaces, and vector spaces over finite fields. Applications to spectral graph theory, rankings, error correcting codes, linear regression, Fourier transforms, principal component analysis, and solving univariate polynomial equations. Prerequisite: a minimum grade of 2.7 in either MATH 208 or MATH 308, or a minimum grade of 2.0 in MATH 136.