Question

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

\[A= UDV\]

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.