## Everything you need to know about transposing matrices and symmetric matrices

Matrix transposes and symmetric matrices are linked — in fact, the definition of a symmetric matrix is that a symmetric matrix A’s transpose gives back the same matrix A.

This is a continuation of my linear algebra series, tied with the 18.06 MIT OCW Gilbert Strang course on introductory linear algebra. Let’s jump right in with the basics on transposes.

## Transposing a matrix

We transpose a two-dimensional matrix by using it’s rows as columns, or inversely, as it’s columns as rows. That is all it takes to do the simple operation.