Euclidean Norm

ahamdiheme

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

Fredrik

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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ahamdiheme	Euclidean Norm Tweet 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

Fredrik Mentor	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 ≤...