Lecture 19

10 Maio 2022, 10:00 • Alexandra Symeonides

Invariance of the rank under elementary row operations. Gaussian elimination method for the calculus of the rank. Square matrices: identity matrix and inverse matrix. Uniqueness of the inverse matrix.

Relation between invertibility of a square matrix and rank, inverse matrix by Gauss reduction

method. Properties regarding powers, inverse and transpose of a square matrix.
Ex 16 (c) ex 17 (b)

---

Lecture 18

9 Maio 2022, 10:00 • Alexandra Symeonides

The vector space of matrices Mn m(R): sum between matrices and product by a scalar

number. Null matrix; line and column matrices; (upper and lower) triangular and diagonal

matrices. Transposition and symmetric matrices. Product of matrices, powers of matrices.

Rank of matrix: definition; invariance under transposition.

---

Practical session 11

5 Maio 2022, 14:30 • Alexandra Symeonides

Linear Algebra: exercise 1. (d), 2. (b)(c)(f), 6. (c)(d), 8.

---

Lecture 17

3 Maio 2022, 10:00 • Alexandra Symeonides

Basis and coordinates. Examples and exercises (2. (d), 4. (a), 6. (a)). Canonical basis and dimension. Important results and consequences about basis. 

---

Lecture 16

2 Maio 2022, 10:00 • Alexandra Symeonides

Linear combinations and linear independence. Linear span of a set of vectors, vector subspace, notion of basis. Examples.

---