R: power transform of a matrix

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 2.0-0 Index]