II. Matrices and determinants. |
1. Matrices.
1.1 Basic definitions.
1.2 Operations with matrices.
1.3 Special matrices.
2. Determinants.
2.1 Preliminars on permutacions.
2.2 Determinant of a square matrix: definition and properties.
2.3. Development of a determinant by adjoints.
2.4. Rank of a matrix.
2.5. Inverse of a matrix.
3. Equivalence and congruence of matrices.
3.1 Elementary transformations.
3.2 Row equivalence of matrices.
3.3 Column equivalence of matrices.
3.4 Matrix equivalence.
3.5 Matrix congruence.
4. Systems of linear equations.
4.1 Cramer's rule.
4.2 Rouche-Frobenius' Theorem.
4.3 Gaussian elimination. |