Description Usage Arguments Details Value Author(s) Examples

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

1 2 | ```
powerofpsdmatrix( M , p,...)
``` |

`M` |
a matrix, preferably symmetric |

`p` |
a single number giving the power |

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

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.

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

where the `UDP`

is the singular value
decomposition of M.

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

1 2 3 | ```
data(SimulatedAmounts)
d <- ilr(sa.lognormals)
var( d %*% powerofpsdmatrix(var(d),-1/2)) # Unit matrix
``` |

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