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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:

Square matrix example

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:

Diagonal matrix example

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

Row matrix

A matrix with one row is called a row matrix

Example 3:

Row matrix example

Column matrix

A matrix with one column is called a column matrix

Example 4:

Column matrix example

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: transpose of a matrix example

0-matrix

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

Example 6:

0 - matrix example

An identity matrix I

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

Example 7:

identity matrix example

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:

opposite matrix definition opposite matrix definition

A symmetric matrix

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

Example 9:

symmetric matrix definition