# [R] A function for raising a matrix to a power?

(Ted Harding) ted.harding at nessie.mcc.ac.uk
Sun May 6 12:35:41 CEST 2007

```[Apologies: This will probably break the thread, but at the moment
I cannot receive mail since my remote mail-server is down, and so
am responding to the message as found on the R-help archives;
hence this is not a "Reply"]

From:
Atte Tenkanen attenka at utu.fi
Sun May 6 11:07:07 CEST 2007

> Is there a function for raising a matrix to a power? For example if you
> like to compute A%*%A%*%A, is there an abbreviation similar to A^3?
>
> Atte Tenkanen
>
> > A=rbind(c(1,1),c(-1,-2))
> > A
>      [,1] [,2]
> [1,]    1    1
> [2,]   -1   -2
> > A^3
>      [,1] [,2]
> [1,]    1    1
> [2,]   -1   -8
>
> But:
>
> > A%*%A%*%A
>      [,1] [,2]
> [1,]    1    2
> [2,]   -2   -5

Of course, "^" alone acts element-wise on the matrix A, so the result
of A^3 is the matrix B where B[i,j] = A[i,j]^3.

However, you can write your own, and call it for instance "%^%":

"%^%"<-function(A,n){
if(n==1) A else {B<-A; for(i in (2:n)){A<-A%*%B}}; A
}

Then:

> A
[,1] [,2]
[1,]    1    1
[2,]   -1   -2

> A%^%1
[,1] [,2]
[1,]    1    1
[2,]   -1   -2

> A%^%2
[,1] [,2]
[1,]    0   -1
[2,]    1    3

> A%^%3
[,1] [,2]
[1,]    1    2
[2,]   -2   -5

> A%^%100
[,1]          [,2]
[1,] -1.353019e+20 -3.542248e+20
[2,]  3.542248e+20  9.273727e+20

Hoping this helps!
Ted.

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Date: 06-May-07                                       Time: 11:35:31
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