The columns of $U$ are left-singular vectors (eigenvectors of $AA^T$); columns of $V$ are right-singular vectors (eigenvectors of $A^T A$)

For full column rank, $\Sigma$ is $n \times n$ and invertible

The singular values (diagonal of $\Sigma$) are always real and non-negative

$U$, $\Sigma$, and $V$ are uniquely determined by $A$