# [R] nth root of matrix

Spencer Graves spencer.graves at structuremonitoring.com
Wed Jul 3 08:30:01 CEST 2013

```
On 7/2/2013 9:24 PM, David Winsemius wrote:
> On Jul 2, 2013, at 8:11 PM, Sachinthaka Abeywardana wrote:
>
>> Hi all,
>>
>> I want to do the following:
>>
>> a=matrix(c(-1,-2,-3))
>> a^(1/3) #get 3rd root of numbers[,1]
>>
>> [1,]  NaN
>> [2,]  NaN
>> [3,]  NaN
>>
>>
>> All I get is NaNs, what is the proper way of doing this? Would like to
>> retain the fact that it is a matrix if possible (not a requirement
>> though).
> ?complex
>
>   a=matrix(c(-1+0i,-2+0i,-3+0i))

I tried that.  The problem is that there are 3 different cube
roots in the complex plane, and a^(1/3) only gives one of them.  See
Wikipedia, "roots of unity" or the examples in the help file for
"newton_raphson {elliptic}".

I assume that Sachinthaka wants the real roots.  Try the following:

n <- 3 # n must be an odd integer for this to work
a=matrix(c(-1,-2,-3))
as <- sign(a)
ab <- abs(a)
cr <- as*(ab^(1/n))
> cr
[,1]
[1,] -1.000000
[2,] -1.259921
[3,] -1.442250
cr^n

Hope this helps.  Spencer Graves

> David Winsemius
> Alameda, CA, USA
>
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