Once you have the proof for triangular inequality for any two vectors, the result should automatically follow.
Note that Wx and Wy are themselves vectors.
So ||W(x+y)|| = ||Wx+Wy|| <= || Wx|| + ||Wy||
I guess thats it ..
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.