# Moore-Penrose pseudoinverse

### 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 valuesCompute

*\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 |

Want to suggest features or report bugs for rdrr.io? Use the GitHub issue tracker. Vote for new features on Trello.