| 1 | Set algebra, transformations, some algebraic structures, permutations, polynomials. | [1] p.1-14 |
| 2 | Definitions and some basic concepts, matrix operations. | [1] p.18-33 |
| 3 | Matrix multiplications, transpose of a matrix, some special matrices and their specialties. | [1] p.36-59 |
| 4 | Elementary operations and elementary matrices. | [1] p.78-88 |
| 5 | By using elementary matrix operations, finding an inverse of a matrix, equivalent matrices and their applications. | [1] p.89-100 |
| 6 | Determinants, and their elementary properties, calculation of determinants by using Minors, determinants by using permutations, determinant of a matrix multiplication. | [1] p.117-130 |
| 7 | Sarrus rule, Adjoint of square matrix, finding inverse of a matrix by using blocks. | [1] p.134-146 |
| 8 | System of linear equations and related matrices, finding rank of a matrix by elementary row operations. | [1] p.160-165 |
| 9 | Some criterias related to the existence of a system of a linear equations, solution of system of linear equations, solution of a homogenous system. | [1] p.166-197 |
| 10 | Vector spaces and related definitions and some basic operations on vector spaces, subspaces and , lineer independence and dependence, bases and dimension. | [1] p.216-238 |
| 11 | Coordinates of a vector related to a specific bases, row and coloumn ranks,rank of a square matrix and its relation to determinants. | [1] p.239-263 |
| 12 | Inner products, vector norms, distance between two vectors, an angle between two vectors, orthogonal vectors. | [1] p.284-296 |
| 13 | Characteristic polynomial, eigenvalues and eigenvectors, eigenspace, Cayley-Hamilton theorem and its application for finding inverse of a matrix, finding eigenvalues of a matrix by matrix norms and application to sustainable engineering, singular values | [1] p.444-491 |
| 14 | Similar matrices and diagonalization and its applications, diagonalization of symmetric matrices. | [1] p.502-523 |