Search All of the Math Forum:

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Every Subspace of R^N has an Orthogonal Basis?
Replies: 175   Last Post: Jul 4, 2006 9:20 AM

 Messages: [ Previous | Next ]
 Denis Feldmann Posts: 533 Registered: 4/23/06
Re: Every Subspace of R^N has an Orthogonal Basis?
Posted: Jun 29, 2006 11:29 AM

Hatto von Aquitanien a écrit :
> Denis Feldmann wrote:
>

>> Hatto von Aquitanien a écrit :
>
>> Of course you are trolling,
>
> Uh, no. I'm very much attempting to engage in honest dialog.

>
>> but it will be hard, even for you, to
>> explain that the slight detail of forgetting to define the operations of
>> your vector space doesn't matter at all here.

>
> Hu? Do you know how to work with vectors in a Euclidian a plane?

It happens I do. But your thing is not yet an Euclidian space. What isq
the formuma or the metric?

If so,
> that's all you need to know. If you want the math to produce the mapping,
> it's trivial.

If you say so...

>
>> While we are on it, I
>> wonder why you insist on suppressing the north pole : a slight (or tot
>> so slight) complication of the map would take care of that.

>
> Unless I use the notion which I presented in my earlier post, of splitting
> the neighborhood of the north pole and wrapping it around infinity, I don't
> see how I can produce a complete bijective map.

Cantor-Bernstein

>
>> And of
>> course, there is no way you would get a subspace of R^3, but then again
>> this is not to bother you, is it?

>
> Well, I'm not convinced of that.

At this stage, it is clear you are trolling. No one could be *that* dumb...

I have not insisted that I can do such a
> thing in a way that would be acceptable to others. Nonetheless, if the
> mapping is isomorphic to Euclidian R^2, then I have an equivalence relation
> between the coordinate system on the sphere and the Euclidian plane. It
> appears to be a matter of whether people accept that as justification for
> calling the mapping on the sphere a subspace R^3. At this point, I really
> don't care.

Thois is what tyou call "honest dialog"? *plonk*

>

Date Subject Author
6/26/06 Hatto von Aquitanien
6/26/06 Lee Rudolph
6/26/06 Jose Carlos Santos
6/26/06 Hatto von Aquitanien
6/26/06 Jose Carlos Santos
6/26/06 Hatto von Aquitanien
6/26/06 magidin@math.berkeley.edu
6/26/06 Robert Low
6/26/06 James Dolan
6/26/06 Hatto von Aquitanien
6/26/06 magidin@math.berkeley.edu
6/26/06 Hatto von Aquitanien
6/26/06 magidin@math.berkeley.edu
6/26/06 Hatto von Aquitanien
6/26/06 magidin@math.berkeley.edu
6/27/06 Hatto von Aquitanien
6/27/06 Virgil
6/27/06 Hatto von Aquitanien
6/27/06 Gene Ward Smith
6/27/06 Hatto von Aquitanien
6/28/06 Brian Quincy Hutchings
6/27/06 Michael L. Siemon
6/27/06 Hatto von Aquitanien
6/27/06 Michael L. Siemon
6/27/06 Virgil
6/27/06 magidin@math.berkeley.edu
6/27/06 Tim Golden http://bandtech.com
6/27/06 magidin@math.berkeley.edu
6/28/06 David C. Ullrich
6/28/06 Tim Golden http://bandtech.com
6/28/06 magidin@math.berkeley.edu
6/28/06 Tim Golden http://bandtech.com
6/29/06 Robert Low
6/29/06 Tim Golden http://bandtech.com
6/29/06 David C. Ullrich
6/27/06 Dave Seaman
6/27/06 Hatto von Aquitanien
6/27/06 David C. Ullrich
6/27/06 Hatto von Aquitanien
6/27/06 David C. Ullrich
6/27/06 magidin@math.berkeley.edu
6/26/06 Virgil
6/29/06 Pinky
6/29/06 Hatto von Aquitanien
6/26/06 Gene Ward Smith
6/27/06 Hatto von Aquitanien
6/27/06 Virgil
6/27/06 Hatto von Aquitanien
6/27/06 Gene Ward Smith
6/27/06 Hatto von Aquitanien
6/27/06 Gene Ward Smith
6/27/06 Gene Ward Smith
6/27/06 Hatto von Aquitanien
6/27/06 Gene Ward Smith
6/27/06 Mariano
6/26/06 Virgil
6/27/06 Hatto von Aquitanien
6/27/06 Virgil
6/27/06 Hatto von Aquitanien
6/27/06 Virgil
6/28/06 Hatto von Aquitanien
6/28/06 David C. Ullrich
6/28/06 Hatto von Aquitanien
6/29/06 David C. Ullrich
6/29/06 Hatto von Aquitanien
6/29/06 David C. Ullrich
6/29/06 Lee Rudolph
6/29/06 K. E. Pledger
6/29/06 Hatto von Aquitanien
6/29/06 Denis Feldmann
6/29/06 Hatto von Aquitanien
6/29/06 Denis Feldmann
6/29/06 Hatto von Aquitanien
6/29/06 Virgil
6/29/06 magidin@math.berkeley.edu
6/29/06 David C. Ullrich
6/29/06 Gene Ward Smith
6/29/06 Hatto von Aquitanien
6/29/06 magidin@math.berkeley.edu
6/29/06 Hatto von Aquitanien
6/28/06 magidin@math.berkeley.edu
6/27/06 David C. Ullrich
6/26/06 Jose Carlos Santos
6/26/06 David C. Ullrich
6/26/06 Robert Low
6/26/06 David C. Ullrich
6/26/06 David C. Ullrich
6/26/06 Hatto von Aquitanien
6/26/06 Robert Low
6/26/06 magidin@math.berkeley.edu
6/26/06 Hatto von Aquitanien
6/26/06 David C. Ullrich
6/27/06 kunzmilan@atlas.cz
6/27/06 Hatto von Aquitanien
6/27/06 Robert Low
6/27/06 Lee Rudolph
6/27/06 Denis Feldmann
6/27/06 Hatto von Aquitanien
6/27/06 Robert Low
6/28/06 David C. Ullrich
6/28/06 Hatto von Aquitanien
6/29/06 David C. Ullrich
6/29/06 Hatto von Aquitanien
6/29/06 Virgil
6/30/06 Hatto von Aquitanien
6/30/06 Denis Feldmann
6/30/06 Hatto von Aquitanien
6/30/06 Denis Feldmann
6/27/06 Hatto von Aquitanien
6/28/06 Robert Low
6/27/06 Denis Feldmann
6/27/06 David C. Ullrich
6/27/06 Virgil
6/28/06 Hatto von Aquitanien
6/28/06 Robert Low
6/28/06 Hatto von Aquitanien
6/28/06 Robert Low
6/28/06 Gene Ward Smith
6/28/06 Hatto von Aquitanien
6/28/06 Hatto von Aquitanien
6/28/06 Lee Rudolph
6/28/06 Mariano
6/28/06 Mariano
6/29/06 Lee Rudolph
6/29/06 magidin@math.berkeley.edu
6/29/06 Shmuel (Seymour J.) Metz
6/29/06 Lee Rudolph
6/30/06 Bertie Reed
6/30/06 Denis Feldmann
6/30/06 Mariano
6/30/06 Denis Feldmann
6/30/06 Mariano
6/30/06 Aatu Koskensilta
7/2/06 Shmuel (Seymour J.) Metz
7/2/06 Herman Rubin
7/2/06 Denis Feldmann
6/29/06 Mariano
6/29/06 Gene Ward Smith
6/28/06 David C. Ullrich
6/29/06 Hatto von Aquitanien
6/29/06 Virgil
6/29/06 Robert Low
6/29/06 Lee Rudolph
6/29/06 Virgil
6/29/06 Lee Rudolph
6/29/06 Virgil
6/29/06 W. Dale Hall
6/30/06 Robert Low
6/30/06 Virgil
6/30/06 Hatto von Aquitanien
6/30/06 Virgil
6/30/06 Hatto von Aquitanien
6/30/06 magidin@math.berkeley.edu
7/1/06 Hatto von Aquitanien
7/1/06 magidin@math.berkeley.edu
7/2/06 Hatto von Aquitanien
7/2/06 Denis Feldmann
7/2/06 David C. Ullrich
7/2/06 Hatto von Aquitanien
7/2/06 magidin@math.berkeley.edu
7/3/06 Gerry Myerson
7/3/06 Hatto von Aquitanien
7/3/06 David C. Ullrich
7/3/06 magidin@math.berkeley.edu
7/3/06 Hatto von Aquitanien
7/3/06 magidin@math.berkeley.edu
7/3/06 Hatto von Aquitanien
7/3/06 Virgil
7/3/06 David C. Ullrich
6/30/06 Robert Low
6/29/06 Hatto von Aquitanien
6/29/06 Virgil
6/29/06 Hatto von Aquitanien
6/29/06 Virgil
7/4/06 kunzmilan@atlas.cz
7/4/06 Lee Rudolph