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Справка Scilab >> Linear Algebra > linear > pinv

# pinv

pseudoinverse

### Syntax

`pinv(A,[tol])`

### Arguments

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)```

• rank — rank
• svd — singular value decomposition
• qr — QR decomposition

### Used Functions

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

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