
Re: norm
Posted:
Mar 9, 2013 4:58 PM


On Sat, 09 Mar 2013 14:47:45 0500, quasi <quasi@null.set> wrote:
>novis wrote: >>quasi 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. >> >>Well I was talking about A transpose x or A'x. Can you please >>show how x=A'x? > >OK, I missed your use of the symbol ' denoting transpose. > >So A' is a map from R^p to R^q. > >As before, since A is columnwise orthonormal, rank(A) = q, >hence p >= q. > >For x in R^p, A'x is in R^q, and yes, it's true that > > A'x = x.
I don't think so...
>where the norms are the usual Euclidean norms in R^q and R^p >respectively. > >Is this homework? > >In any case, I don't have time to help you on this right now, >maybe tomorrow. > >quasi

