# pinv: Moore-Penrose pseudoinverse In lintools: Manipulation of Linear Systems of (in)Equalities

## Description

Compute the pseudoinverse of a matrix using the SVD-construction

## Usage

 `1` ```pinv(A, eps = 1e-08) ```

## Arguments

 `A` [numeric] matrix `eps` [numeric] tolerance for determining zero singular values

## Details

The Moore-Penrose pseudoinverse (sometimes called the generalized inverse) \boldsymbol{A}^+ of a matrix \boldsymbol{A} has the property that \boldsymbol{A}^+\boldsymbol{AA}^+ = \boldsymbol{A}. It can be constructed as follows.

• Compute the singular value decomposition \boldsymbol{A} = \boldsymbol{UDV}^T

• Replace diagonal elements in \boldsymbol{D} of which the absolute values are larger than some limit `eps` with their reciprocal values

• Compute \boldsymbol{A}^+ = \boldsymbol{UDV}^T

## References

S Lipshutz and M Lipson (2009) Linear Algebra. In: Schuam's outlines. McGraw-Hill

## Examples

 ```1 2 3 4 5 6 7``` ```A <- matrix(c( 1, 1, -1, 2, 2, 2, -1, 3, -1, -1, 2, -3 ),byrow=TRUE,nrow=3) # multiply by 55 to retrieve whole numbers pinv(A) * 55 ```

lintools documentation built on June 6, 2017, 5:04 p.m.