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