Main Page | See live article | Alphabetical index In mathematics, and in particular linear algebra, the pseudoinverse of a matrix is a generalization of the inverse matrix. Usually, the pseudoinverse is computed using singular value decomposition. The pseudoinverse is defined only for matrices whose entries are real or complex numbers. Properties of the pseudoinverse is the unique matrix which satisfies the following criteria: (That is, is hermitian). Here is the conjugate transpose of a matrix M. If A and B are such matrices that the product is defined and either one of them is unitary, then it holds that . Finding the pseudoinverse of a matrix Let k be the rank of a matrix A. Then A can be decomposed as , where B is a -matrix and C is a matrix. Then . If k is equal to m or n, then B or C can be chosen to as identity matrix and the formula reduces to or . A computationally simpler way to get the pseudoinverse is using the singular value decomposition. If be the singular value decomposition of A, then . For a diagonal matrix such as , we get the pseudoinverse by inverting each non-zero element on the diagonal. Add something about applications here. Least squares? This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.