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

(1)   equation

Example

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

(2)   equation

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 (equation). For example:

    equation