Calculate Rational/Irrational Powers of a Matrix

[Ali Asadullah]

We know how to calculate a integral powers of a matrix but how can we find rational fractional powers and irrational powers??

 

[phyzguy]

The best way is to expand the result in a power series about the identity matrix. Then you can write:
$$M^a = I + a (M-I) + \frac{a(a-1)}{2}(M-I)^2 + ...$$

 

[Ali Asadullah]

I is identity matrix of which order??
Let M is 4$$\times3$$ then what will be the order of I?

 

[Borek]

Let M is 4$$\times3$$

Is it at all possible to calculate any power of a non square matrix? What will be M² in your case?

 

[Ali Asadullah]

Soory Morek