Date: Mar 9, 2013 4:39 AM
Subject: Re: norm
>Suppose A is a p x q columnwise orthonormal matrix and suppose
>x is any vector in R^p. Then what is the relation between
>||x|| and ||Ax|| ?
A is a p x q matrix, so regarded as a function,
A maps R^q to R^p.
x is in R^q
not in R^p as you specified, and
Ax is in R^p
Also, since A is columnwise orthonormal, it follows that
p >= q.
As far as norm comparison, since A is orthonormal,
|Ax| = |x|
where the norms are the usual Euclidean norms in R^p and R^q,