**Problem:**
Prove that if W is an arbitrary nonsingular matrix, the function

defined by:

is a vector norm.

**------------------------------------------------------------------------------------** **Attempt:**
The only thing I can think of is to go through the conditions a vector norm must satisfy, and check that it holds for a 2-norm..

__1. condition:__
If I look at the 2-Norm, I get:

__2. condition:__ __3. condition:__
Since

and

we have

__4. condition:__
If

Here you need to prove that ...here is where you need very strongly the condition that is a non-singular matrix. Tonio
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I am pretty sure that this should be done without using any specific norm, but I do not know how.

Thank you for your time.