compositions (version 1.01-1)

powerofpsdmatrix: 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

Value

• U%*% D^p %*% t(P) where the UDP is the singular value decomposition of M.

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.

Examples

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