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

Charles C. Berry cberry at tajo.ucsd.edu
Sun Apr 27 19:00:34 CEST 2008

```On Sun, 27 Apr 2008, jmrossbach wrote:

>
> 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

?eigen

as in

emat <- eigen( R )
emat\$vectors %*%diag(emat\$values^(-1/2)) %*% t(emat\$vectors)

Or if you do not need a symmetric result

?chol
?backsolve

The usual advice given to a question along these lines (inverting a
matrix) is to be sure you really needed to do it explicitly. If you are
solving a system of equations there are often better methods to do it
involving matrix decompositions.

HTH,

Chuck

>
> Thank you so much.
> --
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