Eigenvalues, eigenvectors, generalized eigenvectors, minimal/characteristic polynomial, Jordan normal/canonical form, companion matrix and rational canonical form, inner products, adjoint of a linear map, positive-definite operators and isometries, polar decomposition and singular-value decomposition, exponential of a matrix and applications to differential equations, least squares and curve fitting, bilinear and quadratic forms, dual spaces and transpose of a matrix, quotient spaces, multilinear maps, tensor products. Prerequisite: MATH 3330 or consent of instructor.