quasi
Posts:
11,740
Registered:
7/15/05


Re: norm
Posted:
Mar 9, 2013 4:39 AM


novis wrote: > >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.
Thus,
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, respectively.
quasi

