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Topic: norm
Replies: 8   Last Post: Mar 10, 2013 1:45 PM

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Posts: 46
Registered: 7/19/08
Re: norm
Posted: Mar 9, 2013 12:37 PM
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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||?

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