Topic 2. Matrices, determinants and systems of linear equations |
Matrix operations: addition, scalar multiplication and product of matrices. Matrix inverse. LU decomposition. Block matrices. Determinants. Systems of linear equations. The matrix equation Ax=b. Solution set of a system of linear equations. The matrix of a system of linear equations. Elementary row operations and Gauss' method. Numerical methods for the systems of linear equations. |
Topic 4. Matrix diagonalization. |
Eigenvalues and eigenvectors. Eigenspace. Matrix diagonalization and diagonalizable matrices. |