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Topic: Failing Linear Algebra:
Replies: 54   Last Post: Jan 10, 2007 12:47 PM

 Messages: [ Previous | Next ]
 Russell Blackadar Posts: 586 Registered: 12/12/04
Re: Failing Linear Algebra:
Posted: May 1, 2004 9:23 AM

Another correction! This is good, I'm learning stuff. I think this
will be the last one or I risk looking a bit too much like JSH.

On Thu, 29 Apr 2004 19:40:06 -0700, russell@mdli.com wrote:

[basis for kernel -- mine -- vs. bogus basis for solution set -- his]

>My vectors are a basis -- of the kernel, not of the solution set
>(which has no basis). Yours are not a basis of any space relevant to
>the problem, AFAICS.

They're not a basis of any relevant *subspace* of our domain. But
just for the record, I realize now that it *is* a basis for a 3D
vector space that has + and * redefined to transform first into the
kernel space, perform the operation normally there, and transform
back; and that *is* a relevant vector space (namely, it is a vector
space of all solution vectors). And that isn't the only way one could
define + and * to generate the same solution set from that basis; but
I think I've digressed far enough here... If Anonymous has any clue what
I mean with all this, he will be doing very well indeed, otherwise not
to worry.

Lesson: in math, one should never assert the nonexistence of
something just because one has failed to think of an example.

[snip to R^2 example]

>You see the trouble your method got you into. Forget trying to get a
>basis for your solution set -- it isn't a vector space!

Not a vector space with the usual +,* operations of R^2, that is.

Date Subject Author
4/22/04 Guest
4/22/04 Michael N. Christoff
1/10/07 Gerry Myerson
1/10/07 Jonathan Miller
1/10/07 Guest
1/10/07 David C. Ullrich
1/10/07 Acid Pooh
1/10/07 Guest
4/23/04 Brian Borchers
4/27/04 Guest
1/10/07 maky m.
4/26/04 David Ames
1/10/07 Guest
1/10/07 Michael Stemper
1/10/07 maky m.
4/23/04 Porker899
4/27/04 Guest
1/10/07 Abraham Buckingham
1/10/07 Mitch Harris
1/10/07 Guest
1/10/07 Grey Knight
1/10/07 Guest
1/10/07 Toni Lassila
1/10/07 Thomas Nordhaus
1/10/07 George Cox
4/28/04 Dave Rusin
4/28/04 George Cox
4/28/04 George Cox
4/29/04 Marc Olschok
4/29/04 Mitch Harris
4/29/04 Robert Israel
4/28/04 Guest
4/29/04 Guest
1/10/07 Dave Rusin