Singular value decomposition

Singular value decomposition (SVD)

Let A be an $m\times n$ matrix. SVD decomposes $A$ as:

where $U$ and $V$ are [what type?] matrices and $\mathrm{\Sigma }$ is a [what type?] matrix with non-negative real numbers on the diagonal. The diagonal entries of $\mathrm{\Sigma }$ are called the singular values of $A$.