Matrix Operations. Matrix Inverses, Smith Normal Form. LU-Factorization, PLU-Factorization. Determinant and Invertibility, Cramer's Rule. Eigenvalues and Eigenvectors. Diagonalization, Multiplicity Theorems. Subspaces and Spanning, Null Space, Image Space, Eigenspace. Independence and Dimension. Orthogonality, Expansion Theorem. Rank of a Matrix, Nullity, Rank-Nullity Theorem. Similarity and Diagonalization, Symmetric Matrices. Best Approximation and Least Squares. Orthogonal Diagonalization, Principal Axes Theorem. Positive Definite Matrices, Cholesky Factorization. QR-Factorization, Power Method. Singular Value Decomposition, Pseudoinverse, Penrose Theorem. Unitary Diagonalization, Schur's Theorem, Spectral Theorem. Note: Not to be taken for credits with MATH 432