Singular Value Decomposition

Another important matrix decomposition is singular value decomposition or SVD. For any $m \times n$ matrix $A$, we may write:

where $U$ is a unitary (orthogonal in the real case) $m \times m$ matrix, $D$ is a rectangular, diagonal $m \times n$ matrix with diagonal entries $d_1,...,d_m$ all non-negative. $V$ is a unitary (orthogonal) $n \times n$ matrix. SVD is used in principle component analysis and in the computation of the Moore-Penrose pseudo-inverse.