video

If $A \in \mathbb{R}^{m \times n}$ is any $m \times n$ matrix, it can be decomposed as

$A = U D V^T$

where $U$ is $m \times n$, $D$ is $n\times n$ and $V$ is $n \times n$, and $D$ is diagonal.

The diagonal elements of $D$are called the singular values.

The columns of $U$ are the eigenvectors of $AA^T$

The columns of $V$ are the eigenvectors of $A^T A$

In Matlab it's the svd command. Subtletly with fat matrices

Good explanation of the intuition