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 > >addition; > >(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.
So now we know (if we didn't already) why you're failing linear algebra. Read a text book (in case your notes from the lectures are incomplete or wrong) and learn those definitions.
-- G.C. Note ANTI, SPAM and invalid to be removed if you're e-mailing me.