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Euclidean Normby ahamdiheme
Tags: properties of norm 
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#1
Dec1008, 03:06 AM

P: 26

I just want to verify if the following is correct
[tex]\left\right\x\[/tex]_{2}.[tex]\left\right\A\[/tex]_{2}= [tex]\left\right\Ax\[/tex]_{2} Thanks 


#2
Dec1008, 03:24 AM

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P: 9,340

How are you defining the norm of the operator? As [itex]Tr(A^TA)[/itex]? In that case, no. If you let x=(1,0,...,0), the righthand side only contains components from the first column of A but the lefthand side contains other components.
However, the norm of A is often defined as [tex]\A\=\sup_{\x\=1}\Ax\[/tex] so maybe if you change the = to ≤... 


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