I've been researching the bibliography for my paper, which I am hoping will form the mathematical basis for what other people do. I'm a proponent of the idea that one-line books and papers should be cited when possible, due to their availability, and I found the above, nearly complete book on multilinear algebra. It makes less demands on the mathematical sophistication of the reader than the standard references of Greub's "Multilinear Algebra", or Bourbaki.

Best of all, it is *free* and *on line*. If someone wants to learn more about wedge products (also often, as in this book, called exterior products) then chapter 2 of this book seems like a good place to start--not to mention the rest of it. You could even learn about the algebra of screws. :)

http://www.ses.swin.edu.au/homes/browne/grassmannalgebra/book/

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:

> If someone wants to learn

more about wedge products (also often, as in this book, called

exterior products) then chapter 2 of this book seems like a good place

to start--not to mention the rest of it. You could even learn about

the algebra of screws. :)

>

> http://www.ses.swin.edu.au/homes/browne/grassmannalgebra/book/

Thanks Gene!

If anyone is still struggling, as I was until a few minutes ago, to

understand what the heck the exterior product is (I prefer this name

to "wedge product"), and what the point of it is, then just read the

first 6 pages of the Introduction. The result was a great "aha!" for

me.

It is really quite a beautiful conception. I still say we don't "need"

it, but I can certainly see that some things will be described much

more elegantly _with_ it.

Thanks guys for all your attempts. What I was missing was

(a) Its geometrical interpretation

"thus enabling us to bring to bear the power of geometric

visualization and intuition into our algebraic manipulations."

(b) The terms "bivector", "trivector" etc. i.e. The fact that the

product of two vectors isn't another vector, and there isn't anything

else you have to do to the basis of the result e.g. (e1/\e2, e2/\e3,

e3/\e1).

I emailed the author, John Browne, (who lives in Melbourne, Australia)

and thanked him and told him briefly what we were using it for.