pinv

Scilab Function
Last update : 25/04/2007

pinv - pseudoinverse

### Calling Sequence

  `pinv(A,[tol])`

### Parameters

- `A` : real or complex matrix
- `tol` : real number

### Description

`X = pinv(A)` produces a matrix `X` of the same dimensions as `A'` such that:

`A*X*A = A, X*A*X = X` and both `A*X` and `X*A` are Hermitian .

The computation is based on SVD and any singular values lower than a tolerance are treated as zero: this tolerance is accessed by `X=pinv(A,tol)` .

### Examples

    A=rand(5,2)*rand(2,4);
    norm(A*pinv(A)*A-A,1)

### See Also

`rank` , `svd` , `qr` ,

### Used Function

`pinv` function is based on the singular value decomposition (Scilab function `svd` ).