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

 Messages: [ Previous | Next ]
 Russell Blackadar Posts: 586 Registered: 12/12/04
Re: Failing Linear Algebra:
Posted: Apr 28, 2004 11:08 PM

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