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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Question about linear algebra matrix p-norm
Replies: 6   Last Post: Jan 9, 2013 2:42 AM

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fl

Posts: 78
Registered: 10/8/05
Question about linear algebra matrix p-norm
Posted: Jan 7, 2013 11:50 PM
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Hi,
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

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