Prove that function is a vector norm.

**Problem:**

Prove that if W is an arbitrary nonsingular matrix, the function defined by:

is a vector norm.

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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

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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.