Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.
|
|
|
Math Forum
»
Discussions
»
sci.math.*
»
sci.math
Notice: We are no longer accepting new posts, but the forums will continue to be readable.
Topic:
Question about linear algebra matrix p-norm
Replies:
6
Last Post:
Jan 9, 2013 2:42 AM
|
 |
|
fl
Posts:
121
Registered:
10/8/05
|
|
Question about linear algebra matrix p-norm
Posted:
Jan 7, 2013 11:50 PM
|
|
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
|
|
|
|
