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

 Messages: [ Previous | Next ]
 Thomas Nordhaus Posts: 433 Registered: 12/13/04
Re: Failing Linear Algebra:
Posted: Apr 27, 2004 4:31 PM

Anonymous schrieb:
>> then you don't know what a basis is. If you can't give the quantifiers
>> for the definition of independence, you won't be able to do a
>> proof using independence.
>>
>> --Dan Grubb

>
>Let me try that one...independence means a group of vectors (in
>homogenous form???)

Bad phrasing: "independence means a group of vectors". That would
translate: "Independence is a group of vectors...", doesn't make much
sence.

Usually you start definitions like: "A <set> is called <term to be
defined> if <this and that holds true>. Here:

(*) A <set of n vecors {v1,v2,...,vn}> is called <linear independent>
if...

>such that if they all equal the zero vector, then

No, if they all equal the zero vector they can't be linearly
independent.

>the only possible way for that is the each coefficient of every vector
>has to equal 0 too.

OK, that sounds better. But what is "that"? And what is "each
coefficient"? You haven't used or mentioned any coefficient yet. Here
is a way of phrasing it:

(* continued): "... given any coefficient c1,c2,...,cn ..." (you have
to give those things a name!) "... c1*v1+c2*v2+...+cn*vn = 0 ..."
(that's the "that") "... implies c1=c2=...=cn=0"

So, now you have a formal definition!
Thomas

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