Date: Jan 7, 2013 11:50 PM
Author: fl
Subject: Question about linear algebra matrix p-norm

I am reading a book on matrix characters. It has a lemma on matrix p-norm. I do not understand a short explaination in its proof part.

The Lemma is: If F is Rnxn and |F|p<1 (p-norm of F), then I-F is non-singular....

In its proof part, it says: Suppose I-F is singular. It follows that (I-F)x=0 for some nonzero x. But then |x\p=|Fx|p implies |F|p>=1, a contradiction. Thus, I-F is nonsingular.

My question is about how it gets:
But then |x\p=|Fx|p implies |F|p>=1

Could you tell me that? Thanks a lot