Register to reply 
Euclidean Normby ahamdiheme
Tags: properties of norm 
Share this thread: 
#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

Emeritus
Sci Advisor
PF Gold
P: 9,247

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 ≤... 


Register to reply 
Related Discussions  
Norm of matrix  Calculus & Beyond Homework  3  
Norm proof help  Calculus & Beyond Homework  1  
Non archimedean norm  Linear & Abstract Algebra  2  
Generalized solutions for the smallest Euclidean norm  Calculus & Beyond Homework  1  
Euclidean and Non Euclidean Space?  Differential Geometry  1 