# [R] Raising a matrix to the (-1/2) power.

Bill.Venables at csiro.au Bill.Venables at csiro.au
Mon Apr 28 01:56:01 CEST 2008

```This is probably as good a way as any way for this kind of problem.
First define a binary operator:

> "%^%" <- function(x, n)
with(eigen(x), vectors %*% (values^n * t(vectors)))

> m <- matrix(c(1, 0.4, 0.4, 1), nrow = 2)
> m
[,1] [,2]
[1,]  1.0  0.4
[2,]  0.4  1.0

> m %^% (-0.5)
[,1]       [,2]
[1,]  1.0680744 -0.2229201
[2,] -0.2229201  1.0680744

Bill Venables
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-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On Behalf Of jmrossbach
Sent: Sunday, 27 April 2008 11:05 PM
To: r-help at r-project.org
Subject: [R] Raising a matrix to the (-1/2) power.

Hi, I need to raise a correlation matrix; R; to the negative one half
power.
i.e. I need to find R^(-1/2)

eg: if R=[{1,.4},{.4,1}], then R^(-1/2)=[{1.0681,-.2229},
{-.2229,1.0681}]where matrix=[{row1},{row2}]

And are there any built in functions to do this?  mtx.exp doesn't work
because it's not raised to a positive integer

Thank you so much.
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