Compute the Power of a Real Symmetric Matrix
mpower computes m^alpha, i.e.
the alpha-th power of the real symmetric
matrix m.
mpower(m, alpha, pseudo=FALSE, tol)
m |
a real-valued symmetric matrix. |
alpha |
exponent. |
pseudo |
if |
tol |
tolerance - eigenvalues with absolute value smaller or equal
to |
The matrix power of m is obtained by first computing the spectral
decomposition of m, and subsequent modification of the resulting eigenvalues.
Note that m is assumed to by symmetric, and only
its lower triangle (diagonal included) is used in eigen.
For computing the matrix power of cor.shrink use
the vastly more efficient function powcor.shrink.
mpower returns
a matrix of the same dimensions as m.
Korbinian Strimmer (https://strimmerlab.github.io).
# load corpcor library
library("corpcor")
# generate symmetric matrix
p = 10
n = 20
X = matrix(rnorm(n*p), nrow = n, ncol = p)
m = cor(X)
m %*% m
mpower(m, 2)
solve(m)
mpower(m, -1)
msq = mpower(m, 0.5)
msq %*% msq
m
mpower(m, 1.234)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.