does there exist the notion of a non-integer power of a matrix? This seems to be accessible via semigroup-theory, yet I have not seen an actual definition so far.
I am not too firm at this right now, but I am curious. Can you give me a sketch of the definition and provide with some introductory information?
Best Answer
If your matrix has positive eigenvalues, then one definition is to take non-integer powers of each eigenvalue (but keep the eigenvectors the same). This is a common definition used to take square roots, for example.