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

[Charles C. Berry]

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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>
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Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901