powerofpsdmatrix {compositions} | R Documentation |

## power transform of a matrix

### Description

Computes the power of a positive semi-definite symmetric matrix.

### Usage

```
powerofpsdmatrix( M , p,...)
```

### Arguments

`M` |
a matrix, preferably symmetric |

`p` |
a single number giving the power |

`...` |
further arguments to the singular value decomposition |

### Details

for a symmetric matrix the computed result can actually be considered as a version of the given power of the matrix fullfilling the relation:

`M^pM^q=M^{p+q}`

The symmetry of the matrix is not checked.

### Value

`U%*% D^p %*% t(P)`

where the `UDP`

is the singular value
decomposition of M.

### Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

### Examples

```
data(SimulatedAmounts)
d <- ilr(sa.lognormals)
var( d %*% powerofpsdmatrix(var(d),-1/2)) # Unit matrix
```

[Package

*compositions*version 2.0-8 Index]