| Weeks | Topics |
| 1 |
Vector notation, description and properties of vector arithmetic, Linear combinations, scalar product and vector norm, Cross product and its properties.
|
| 2 |
Projection of a vector on a vector, the least squares approximation, Planes.
|
| 3 |
Matrix notation, Representation of linear system equations by matrices, Gauss Elimination method for the solution of linear system equations and realization of this method by matrices, special cases confronted with solving linear system of equations.
|
| 4 |
Rules for matrix operations, Some matrix types and its properties, Computation of matrix inverse: Gauss-Jordan elimination method.
|
| 5 |
Matrix decomposition: A = LU, A = LDU, A = LDLT.
|
| 6 |
Definition of vector spaces, Four fundamental subspaces for matrix: Row, column, null and left null subspaces, Rank of a matrix, The solution of m linear equations in n unknowns for the case of n > m, i.e. under determined system case.
|
| 7 |
Linear independence, base and dimension, Orthogonality of four fundamental subspaces, The solution of m equations in n unknowns for the case of m > n, i.e. over determined system case: Projection on subspaces and the least squares approximation.
|
| 8 |
Orthogonal base vectors and Gram-Schmidt orthogonalization method, Definition of Determinants and its properties.
|
| 9 |
Eigenvalues and eigenvectors for matrices.
|
| 10 |
Diagonalization, The solution of differential equations by eigenvalues and eigenvectors and exponential of a matrix.
|
| 11 |
Complex-value matrices: Symmetric – Hermitian and Orthogonal – Unitary matrix concepts, Positive definite matrices.
|
| 12 |
Singular Value Decomposition (SVD): Decomposition method of m × n matrices for m≠ n.
|
| 13 |
Singular Value Decomposition (SVD): Decomposition method of m × n matrices for m≠ n.
|
| 14 |
Pseudo-inverse of a matrix, Applications: Image processing and effective rank computation
|