pow for real matrices

[Koichi Hashimoto]

Will someone tell me the algorithm in octave used to compute A^r,
where A is a real matrix with positive determinant and r is a real
value (not integer)?

Looking at xpow.cc I think it uses something like the following code:

[V, D]=eig(A);
Dr=D^r;
Ar=V*Dr/V;

and I think it is reasonable because if r=1/n then Ar^n=A.

Will you give me a theoretical background of this algorithm?  Also I
would like to know why Ar becomes a real matirix even if D contains
imaginary part.

Koichi Hashimoto
  Department of Systems Engineering,
  Okayama University



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