MATH 318 AC: 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: either a minimum grade of 2.7 in MATH 208, or a minimum grade of 2.0 in MATH 136.