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a bound for 2-norm matrix

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jane08

Post subject: a bound for 2-norm matrix

Posted: Fri, 4 Mar 2011 14:30:14 UTC

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Joined: Sun, 24 Jan 2010 07:19:31 UTC
Posts: 19

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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Shadow

Post subject: Re: a bound for 2-norm matrix

Posted: Fri, 4 Mar 2011 14:32:25 UTC

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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12172
Location: Austin, TX

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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jane08

Post subject: Re: a bound for 2-norm matrix

Posted: Fri, 4 Mar 2011 14:34:01 UTC

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Joined: Sun, 24 Jan 2010 07:19:31 UTC
Posts: 19

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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