Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|improve this question

3 Answers 3

up vote 1 down vote accepted

There are a few definitions for functions of matrices. See for instance http://en.wikipedia.org/wiki/Matrix_function .

share|improve this 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.

share|improve this answer
    
The more general condition is that the eigenvalues should not be negative numbers; see e.g. this. –  J. M. Apr 18 '13 at 16:30

You can use the binomial series to define powers for appropriate matrices.

share|improve this answer
    
Does the square root of a matrix defined with this approach coincide with the canoical square root $\sqrt(A^\ast A )$? –  shuhalo Jan 14 '11 at 3:46

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.