Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
kaushik.sinha.cs@gmail.com

Posts: 46
Registered: 7/19/08
Re: norm
Posted: Mar 9, 2013 12:37 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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||?



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.