Given a matrix , the transpose of it is written as and is obtained by taking the rows of as columns and the columns of as rows:

(1)

**Example**

Given the following 2×3 matrix, let us find the transpose:

(2)

We see that the transpose of the 2×3 matrix is a 3×2 matrix.

**Symmetric matrices**

A matrix is symmetric if its transpose is equal to itself (). For example: