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

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Virgil

Posts: 1,775
Registered: 12/6/04
Re: Every Subspace of R^N has an Orthogonal Basis?
Posted: Jun 30, 2006 2:09 AM
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In article <Ssmdnf9hNKUwITnZnZ2dnUVZ_q6dnZ2d@speakeasy.net>,
Hatto von Aquitanien <abbot@AugiaDives.hre> wrote:

> Virgil wrote:
>

> > It was, I believe, the sphere x^2 + y^2 + (z-1)^2 = 1 in R^3 which
> > Hatto himself originally referred to, with and without the point
> > (0,0,2). Or possibly one with a different radius but still tangent to
> > the x-y plane.

>
> My original example was slightly in error because I put the center at the
> origin. Hence my comment about it being in need of a trivial modification.
> The model I used to generate the graphics put the center at z=0.5 with a
> radius of 1.


So your modification conforms to my model with r = 0.5


Date Subject Author
6/26/06
Read Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Lee Rudolph
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Jose Carlos Santos
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Jose Carlos Santos
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
James Dolan
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Gene Ward Smith
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Brian Quincy Hutchings
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Michael L. Siemon
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Michael L. Siemon
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Tim Golden http://bandtech.com
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Tim Golden http://bandtech.com
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Tim Golden http://bandtech.com
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Tim Golden http://bandtech.com
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Dave Seaman
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Pinky
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Gene Ward Smith
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Gene Ward Smith
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Gene Ward Smith
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Gene Ward Smith
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Gene Ward Smith
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Mariano
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/29/06
Read "dimensionality" v. "dimension" (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Lee Rudolph
6/29/06
Read Re: "dimensionality" v. "dimension" (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
K. E. Pledger
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Denis Feldmann
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Denis Feldmann
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Gene Ward Smith
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Jose Carlos Santos
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
kunzmilan@atlas.cz
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Lee Rudolph
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Denis Feldmann
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Denis Feldmann
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Denis Feldmann
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Denis Feldmann
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Gene Ward Smith
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Lee Rudolph
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Mariano
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Mariano
6/29/06
Read Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Lee Rudolph
6/29/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
magidin@math.berkeley.edu
6/29/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Shmuel (Seymour J.) Metz
6/29/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Lee Rudolph
6/30/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Bertie Reed
6/30/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal
Basis?)
Denis Feldmann
6/30/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Mariano
6/30/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal
Basis?)
Denis Feldmann
6/30/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Mariano
6/30/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal
Basis?)
Aatu Koskensilta
7/2/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Shmuel (Seymour J.) Metz
7/2/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Herman Rubin
7/2/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal
Basis?)
Denis Feldmann
6/29/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Mariano
6/29/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Gene Ward Smith
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Lee Rudolph
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Lee Rudolph
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
W. Dale Hall
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
7/1/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
7/1/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
7/2/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
7/2/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Denis Feldmann
7/2/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
7/2/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
7/2/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
7/3/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Gerry Myerson
7/3/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
7/3/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
7/3/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
7/3/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
7/3/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
7/3/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
7/3/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
7/3/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
7/4/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
kunzmilan@atlas.cz
7/4/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Lee Rudolph

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