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
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 ≤...