Euclidean Norm

  1. 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. jcsd
  3. Fredrik

    Fredrik 10,263
    Staff Emeritus
    Science Advisor
    Gold Member

    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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