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Topic: Failing Linear Algebra:
Replies: 91   Last Post: Jan 10, 2007 12:56 PM

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Russell Blackadar

Posts: 586
Registered: 12/12/04
Re: Failing Linear Algebra:
Posted: Apr 28, 2004 11:08 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 28 Apr 2004 23:28:17 GMT, Anonymous wrote:

>Grubb:
>

>>>I don't understand. A vector is any collection: (x1, ...., x^n) of
>>anything.
>>>In math, the vectors are numbers.

That last sentence is the one he was responding to. The sentence
before it is wrong too, but his comments aren't directed to that.

>>
>>This is wrong. A function can be a vector (usefully so, in fact).
>>A polynomial can be a vector, a sequence can be a vector. In fact,
>>*anything* can be a vector.

>
>Isn't that what I said though?


Sort of, but then why did you say "in math vectors are numbers"?

I said a vector can be a collection of
>anything, even if that "collection" just contains one vector: for example, one
>function, one polynomial, etc, like you say.


That much is OK, but your notation was wrong. You should use braces
{} rather than parentheses when listing the members of a set, and also
your notation implies that a vector space can only have a finite
number of members; in fact that is only rarely true, and is never true
(except for the trivial case {0}) for vector spaces on the fields
you're familiar with. E.g. the set of real numbers is a vector space
and has infinitely many members. One dimension, yes, but infinitely
many members.

Take care that you don't confuse the set of vectors (i.e. the vector
space itself) with the n-tuple representation of one particular vector
in the space according to some basis. The n-tuple is what you write
with parentheses; it may have a lot of components but it is *one*
vector. Btw even here I am not being sufficiently abstract; there
exist infinite-dimensional vector spaces, and for those spaces the
n-tuple representation of individual vectors is not possible.

You made the same mistake in your response to me, where you talked
about (0,1) as if it were two vectors in R^2, instead of a *single*
vector with two components.


Date Subject Author
4/24/04
Read Re: Failing Linear Algebra:
Daniel Grubb
4/24/04
Read Re: Failing Linear Algebra:
Marc Olschok
4/24/04
Read Re: Failing Linear Algebra:
Daniel Grubb
4/24/04
Read Re: Failing Linear Algebra:
Marc Olschok
4/24/04
Read Re: Failing Linear Algebra:
Daniel Grubb
4/24/04
Read Re: Failing Linear Algebra:
Thomas Nordhaus
4/24/04
Read Re: Failing Linear Algebra:
Dave Rusin
4/25/04
Read Re: Failing Linear Algebra:
Jonathan Miller
4/25/04
Read Re: Failing Linear Algebra:
Felix Goldberg
4/24/04
Read Re: Failing Linear Algebra:
Daniel Grubb
4/28/04
Read Re: Failing Linear Algebra:
Tim Mellor
4/28/04
Read Re: Failing Linear Algebra:
James Dolan
4/28/04
Read Re: Failing Linear Algebra:
Daniel Grubb
4/28/04
Read Re: Failing Linear Algebra:
James Dolan
4/28/04
Read Re: Failing Linear Algebra:
Daniel Grubb
4/28/04
Read Re: Failing Linear Algebra:
gersh@bialer.com
4/29/04
Read Re: Failing Linear Algebra:
Daniel Grubb
4/29/04
Read Re: Failing Linear Algebra:
Dave Rusin
4/28/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
4/29/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
4/28/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
David C. Ullrich
4/29/04
Read Re: Failing Linear Algebra:
Dave Rusin
4/28/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Law Hiu Chung
1/10/07
Read Re: Failing Linear Algebra:
Dave Seaman
1/10/07
Read Re: Failing Linear Algebra:
Marc Olschok
1/10/07
Read Re: Failing Linear Algebra:
George Cox
4/28/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Dave Rusin
4/28/04
Read Re: Failing Linear Algebra:
Lee Rudolph
4/28/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
4/28/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Marc Olschok
1/10/07
Read Re: Failing Linear Algebra:
Toni Lassila
4/29/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
M L
1/10/07
Read Re: Failing Linear Algebra:
Thomas Nordhaus
4/30/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
David C. Ullrich
1/10/07
Read Re: Failing Linear Algebra:
Toni Lassila
4/30/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
4/30/04
Read Re: Failing Linear Algebra:
Russell Blackadar
5/1/04
Read Re: Failing Linear Algebra:
Russell Blackadar
1/10/07
Read Re: Failing Linear Algebra:
George Cox
1/10/07
Read Re: Failing Linear Algebra:
Marc Olschok
4/30/04
Read Re: Failing Linear Algebra:
Guest
4/30/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
5/1/04
Read Re: Failing Linear Algebra:
Russell Blackadar
4/27/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Thomas Nordhaus
1/10/07
Read Re: Failing Linear Algebra:
David C. Ullrich
1/10/07
Read Re: Failing Linear Algebra:
Dave Rusin
1/10/07
Read Re: Failing Linear Algebra:
David C. Ullrich
5/9/04
Read Re: Failing Linear Algebra:
James Dolan
5/10/04
Read Re: Failing Linear Algebra:
David C. Ullrich
5/10/04
Read Re: Failing Linear Algebra:
James Dolan
5/10/04
Read Re: Failing Linear Algebra:
David C. Ullrich
5/10/04
Read Re: Failing Linear Algebra:
Marc Olschok
5/10/04
Read Re: Failing Linear Algebra:
David C. Ullrich
4/27/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Thomas Nordhaus
4/27/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
magidin@math.berkeley.edu
1/10/07
Read Re: Failing Linear Algebra:
David C. Ullrich
1/10/07
Read Re: Failing Linear Algebra:
Marc Olschok
1/10/07
Read Re: Failing Linear Algebra:
David C. Ullrich
1/10/07
Read Re: Failing Linear Algebra:
Tim Mellor
4/28/04
Read Re: Failing Linear Algebra:
Daniel Grubb
4/28/04
Read Re: Failing Linear Algebra:
Daniel Grubb
4/27/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
David C. Ullrich
4/28/04
Read Re: Failing Linear Algebra:
Dave Rusin
4/28/04
Read Re: Failing Linear Algebra:
Daniel Grubb
4/27/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Marc Olschok
4/24/04
Read Re: Failing Linear Algebra:
Wayne Brown
4/24/04
Read Re: Failing Linear Algebra:
Thomas Nordhaus
4/24/04
Read Re: Failing Linear Algebra:
David Ames

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