Main Page | See live article | Alphabetical index Matrix decompositions are factorizations of matrices that express them in some canonical form. For example, the singular value decomposition for matrix M is where U is an m-by-m unitary matrix over K, V is an n-by-n unitary matrix over K, and Σ is an m-by-n diagonal matrix whose diagonal entries Σi,i are non-negative real numbers. Most common matrix decompositions are: Cholesky decomposition Jordan decomposition LU decomposition Schur decomposition Singular value decomposition Spectral decomposition QR decomposition This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.