- #1

FOIWATER

Gold Member

- 434

- 12

I am assuming euclidean norms. Since Ax gives us back a vector and x is itself a vector.

So I have that:

$$||A^k|| = \sup_{||x||=1}(||A^{k}x|| : ||x||=1)$$

and

$$||A||^{k} = \sup_{||x||=1}(||Ax|| : ||x||=1)^{k}$$

Not sure what to do with them, though, any hints appreciated. I was thinking triangle inequality.. but I didn't really get anything from it. And I do not know if the triangle inequality applies to this matrix induced norm (although I think it applies to any operation that qualifies as a norm, since it defines norms).