Topic 2. Matrices and determinants. |
Matrix operations: addition, scalar multiplication and product of matrices. Matrix inverse. Block matrices. Determinants. |
Topic 4. Vector spaces and linear transformations. |
Linear independence. Subspaces. Basis. Dimension. Rank of a system of vectors. Introduction to linear transformations. Matrix of a linear transformation. |
Topic 6. Orthogonallity. |
Real Euclidean inner product. Complex Hermitian inner product. Orthogonallity. Gram-Schmidt. Unitary Diagonalization. Singular value decomposition. Matrix rank reduction. The method of least squares. Quadratic forms. |