# Powers of a matrix

1. Jun 12, 2010

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

2. Jun 12, 2010

### phyzguy

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

3. Jun 12, 2010

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

4. Jun 12, 2010

### Staff: Mentor

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

5. Jun 12, 2010