Hi.

Problem:Prove that if is an arbitrary nonsingular matrix, the function defined by (3.3) is a vector norm.

(3.3) .

Attempt:I know that in if a function is a norm it has to have three properties.

(1) ,

(2) and

(3)

(1)

Let .

Since and every , we have that .

Let .

Since and is nonsingular such that for , we have that and so .

(3)

(2)

I do not know how to prove that the Triangle Inequality holds. Hints are greatly appreciated.

Thanks.