MATH 146 is an advanced-level version of MATH 136. Topics includes vector spaces, linear dependence and span, bases and dimension, linear transformations, rank, change of coordinate matrices, and system of linear equations. We also discuss various topics of matrices such as rank, determinants, eigenvalues and eigenvectors, characteristic polynomial, and diagonalization. 

This is a core course for graduate students in Applied Mathematics. It will also be of interest to students in Engineering and Science who wish to understand and use methods from functional analysis. Basic concepts from functional analysis are introduced and illustrated with applications in various areas such as numerical analysis, control theory, boundary value problems for PDEs, and optimization.

Topics include orthogonal and unitary matrices and transformations; orthogonal projections; the Gram-Schmidt procedure; and best approximations and the method of least squares. Inner products; angles and orthogonality; orthogonal diagonalization; singular value decomposition; and other applications will also be explored.