Date: Jan 23, 2013 4:16 AM
Author: Bruno Luong
Subject: Re: About matrix norms

"Martti" wrote in message <kdo9bl$5a8$1@newscl01ah.mathworks.com>...
> I'm looking for matrix norms that would satisfy
>
> xnorm(A) == 1/xnorm(inv(A))
>
> so that after scaling the matrix with the norm,
>
> Asc = A / xnorm(A)
>
> both xnorm(Asc)==1 and xnorm(inv(Asc))==1 .
>
> Seems to be a norm defined as
>
> function [ value ] = xnorm( A )
> %XNORM Matrix norm
> [~, s, ~] = svd(A);
> value = prod(diag(s))^(1/numel(diag(s)));
> end
>


prod(diag(s)) is the same as
sqrt(det(A'*A)) or sqrt(det(A*A'))

Bruno