| 1 | Algebra of sets, transformations, permutations, polynomials. | [1] p.1-14 |
| 2 | Matrices, definitions, matrix algebra, block matrices. | [1] p.18-33 |
| 3 | Transpoze, special matrices, trace, matrix inverse. | [1] p.36-59 |
| 4 | Elementary operations, elementary matrices. | [1] p.78-88 |
| 5 | Matrix inverse with elementary operations, equivalent matrices and applications. | [1] p.89-100 |
| 6 | Determinants, minors, determinants using permutations, determinant of a product. | [1] p.117-130 |
| 7 | Sarrus rule, adjoint, determinant of block matrices, permanents. | [1] p.134-146 |
| 8 | Midterm examination week, definitions, systems of linear equations and matrices, rank. | [1] p.160-165 |
| 9 | Rank of a matrix with elementary row operations, existence criteria of the solution of a system of linear equations, solution methods, homogenous systems and solutions. | [1] p.166-197 |
| 10 | Definition of a vector space, subspaces, linearly dependent and independent vector sets, base and dimension. | [1] p.216-238 |
| 11 | Coordinates of a vector according to a given base, row and column rank, relationship with rank and determinant. | [1] p.239-263 |
| 12 | Inner product, vector norms, distance and angle between two vectors, orthogonal vectors. | [1] p.284-296 |
| 13 | Characteristic polynomial, eigenvalues, eigenvectors, Cayley-Hamilton theorem, singular values, Application to sustainable engineering | [1] p.444-491 |
| 14 | Similar matrices, diagonalization and its applications. | [1] p.502-523 |