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 Post subject: a bound for 2-norm matrix
PostPosted: Fri, 4 Mar 2011 14:30:14 UTC 
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Could someone help me out to find a bound for the matrix norm?

Assume that \|x-y\|_2=\delta, where \| \cdot \|_2 is vector 2-norm, and x,y \in R^n. Then, what's the bound for the following norm (a sharp bound is preferable)

\|x x^T  - y y^T \|_2, where \| \cdot \|_2 is an operator matrix 2-norm (induced matrix 2-norm)


Last edited by jane08 on Fri, 4 Mar 2011 14:32:51 UTC, edited 1 time in total.

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 Post subject: Re: a bound for 2-norm matrix
PostPosted: Fri, 4 Mar 2011 14:32:25 UTC 
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jane08 wrote:
Could someone help me out to find a bound for the matrix norm?

Assume that \|x-y\|_2=\delta, where \| \cdot \|_2 is an operator matrix 2-norm, and x,y \in R^n. Then, what's the bound for the following norm (a sharp bound is preferable)

\|x^T x - y^T y\|_2


Eh? In the first example you have a couple of vectors, the second operators. Is this really the questions?

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 Post subject: Re: a bound for 2-norm matrix
PostPosted: Fri, 4 Mar 2011 14:34:01 UTC 
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Shadow wrote:
jane08 wrote:
Could someone help me out to find a bound for the matrix norm?

Assume that \|x-y\|_2=\delta, where \| \cdot \|_2 is an operator matrix 2-norm, and x,y \in R^n. Then, what's the bound for the following norm (a sharp bound is preferable)

\|x^T x - y^T y\|_2


Eh? In the first example you have a couple of vectors, the second operators. Is this really the questions?


Sorry, I've corrected the mistakes, and reedit the problem.


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