On Mar 9, 3:39 am, quasi <qu...@null.set> wrote: > 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
Well I was talking about A transpose x or ||A'x||. Can you please show how ||x||=||A'x||?