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Euclidean Norm

by ahamdiheme
Tags: properties of norm
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ahamdiheme
#1
Dec10-08, 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
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Fredrik
#2
Dec10-08, 03:24 AM
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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 right-hand side only contains components from the first column of A but the left-hand 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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