Singular Value Decomposition - Applications of The SVD - Pseudoinverse

Pseudoinverse

The singular value decomposition can be used for computing the pseudoinverse of a matrix. Indeed, the pseudoinverse of the matrix M with singular value decomposition is

where Σ+ is the pseudoinverse of Σ, which is formed by replacing every nonzero diagonal entry by its reciprocal and transposing the resulting matrix. The pseudoinverse is one way to solve linear least squares problems.

Read more about this topic:  Singular Value Decomposition, Applications of The SVD

Other articles related to "pseudoinverse":

Block Matrix Pseudoinverse
... In mathematics, block matrix pseudoinverse is a formula of pseudoinverse of a partitioned matrix ...
Moore–Penrose Pseudoinverse - Construction - Updating The Pseudoinverse
... matrix ( for A with full row rank or for full column rank) is already known, the pseudoinverse for matrices related to can be computed by applying the Sherman–Morrison–Woodbury ... However, updating the pseudoinverse in the general rank-deficient case is much more complicated ...
Block Matrix Pseudoinverse - Derivation
... a column-wise partitioned matrix If the above matrix is full rank, the pseudoinverse matrices of it and its transpose are as follows The pseudoinverse requires (n + p)-square matrix inversion ... defined by Interestingly, from the idempotence of projection matrix, we can verify that the pseudoinverse of block matrix consists of pseudoinverse of ...
Moore–Penrose Pseudoinverse
... In mathematics, and in particular linear algebra, a pseudoinverse A+ of a matrix A is a generalization of the inverse matrix ... The most widely known type of matrix pseudoinverse is the Moore–Penrose pseudoinverse, which was independently described by E ... Earlier, Fredholm had introduced the concept of a pseudoinverse of integral operators in 1903 ...
Moore–Penrose Pseudoinverse - Properties - Basic Properties
... If is invertible, the pseudoinverse and the inverse coincide ... The pseudoinverse of a zero matrix is its transpose ... The pseudoinverse of the pseudoinverse is the original matrix ...