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Linear Algebra - Matrices: (lesson 1 of 3)

## Matrices Definitions

### Square matrix:

If a matrix A has n rows and n columns then we say it's a square matrix.

Example 1:

### Diagonal matrix

A diagonal matrix is a square matrix with all de non-diagonal elements 0. The diagonal matrix is completely denoted by the diagonal elements.

Example 2:

The matrix is denoted by diag(1 , 5 , 9)

### Row matrix

A matrix with one row is called a row matrix

Example 3:

### Column matrix

A matrix with one column is called a column matrix

Example 4:

### Matrices of the same kind

Matrix A and B are of the same kind if A has as many rows as B and A has as many columns as B

### The transpose of a matrix

The n x m matrix AT is the transpose of the m x n matrix A if and only if The ith row of A = the ith column of A' for (i = 1,2,3,..n).

Example 5:

### 0-matrix

When all the elements of a matrix A are 0, we call A a 0-matrix.

Example 6:

### An identity matrix I

An identity matrix I is a diagonal matrix with all diagonal element = 1

Example 7:

### The opposite matrix of a matrix

If we change the sign of all the elements of a matrix A, we have the opposite matrix -A.

Example 8:

### A symmetric matrix

A square matrix is called symmetric if it is equal to its transpose.

Example 9: