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

 Messages: [ Previous | Next ]
 Law Hiu Chung Posts: 303 Registered: 12/7/04
Re: Failing Linear Algebra:
Posted: Apr 28, 2004 7:06 PM

Anonymous wrote:
> George:

>>I was taught (33 years ago in the University of Birmingham, UK) that a
>>vector space is
>>(1) a set of elements (the vectors) which form an abelian group under
>>(2) etc....
>>The phrase "commutative group" or "additive group" might have been used
>>instead of "abelian group"--you'll forgive me if I can't quite remember!
>>

> I think you just made me remember what an abelian group is. It's closed under
> its operation, it's associative, commutative, it's got an inverse, and it's got
> the identity element in it. There may be some other condition, since aren't
> all the above needed for any group? I remember something about an abelian
> group forming a table with a diagonal, or something....

> So, basically, "abelian group" is just an easier way of saying "vector space".
> Rather than listing all 8 conditions. But, that assumes the student *knows*
> what an abelian group is.

Well..... there is a big difference....
As you have already listed the 8 conditions, they are required for the
definition of a vector space. However, some of the 8 conditions can be
violated by an abelian group. For example, scalar multiplication is
undefined for an abelian group in general.

It will help you to appreciate their difference if you compare the exact
defintions of these two terms....

>>How do you/US universities/today's commonly used texts define vector
>>space?

> The 8 conditions.

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