This course focuses on the fundamental theoretical properties of matrices. Topics will include a rigorous treatment of vector spaces (linear independence, basis, dimension, and linear transformations), orthogonality (inner products, projections, and Gram-Schmidt process), determinants, eigenvalues and eigenvectors (diagonal form of a matrix, similarity transformations, and matrix exponential), singular value decomposition, and the pseudo-inverse. Essential proof writing techniques and logic will be reviewed and then used throughout the course in exams and written assignments. MATLAB software will be used in some class exercises and homework.
Course all programs:
Applied and Computational Mathematics