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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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Gerry Myerson

Posts: 4,919
Registered: 12/6/04
Re: Every Subspace of R^N has an Orthogonal Basis?
Posted: Jul 3, 2006 1:11 AM
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In article <e89h9r$1dv1$1@agate.berkeley.edu>,
magidin@math.berkeley.edu (Arturo Magidin) wrote:

> Mathematics requires abstraction; but it also requires precision. You
> lack the latter, and you wouldn't know the former if it stripped
> naked, painted itself purple, and stood on top of a piano with a big
> "Hello! I'm abstraction" while yelling at the top of its lungs.


Well, to be fair, I don't think I'd know abstraction, either,
if it carried on like that.

--
Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email)


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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