**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

... In mathematics, block matrix

**Pseudoinverse**... In mathematics, block matrix

**pseudoinverse**is a formula of**pseudoinverse**of a partitioned matrix ...Moore–Penrose

... matrix ( for A with full row rank or for full column rank) is already known, the

**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

... a column-wise partitioned matrix If the above matrix is full rank, the

**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

... In mathematics, and in particular linear algebra, a

**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

... If is invertible, the

**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 ...Main Site Subjects

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