From: Chris Hillman
Newsgroups: sci.math
Subject: Re: Multilinear alg sources
Date: Mon, 2 Mar 1998 01:27:53 -0800
On 2 Mar 1998, ortiz wrote:
> Hi
> While mathematical litterature on linear algebra abounds in books, few
> references are devoted to multilinear algebra (i mean topics like tensor
> products, tensor algebra and especially symmetric and exterior algebras).
> In Lang's 1965 Algebra, these topics are packed into relatively fews pages.
> On the other hand, Greub's treatise provides an extensive treatment of the
> subject but in my opinion the style isn't clear and exposition is'nt
> transparent for me.
> I was wondering if anyone could recommend some *comprehensive* references
> source regarding this matter. Many thanks in advance.
I don't know whether these will be comprehensive enough for you, but try
Takeo Yokonuma, Tensor Spaces and Exterior Algebra
(overly fussy notation, but some good insights on Grassmanians)
V. V. Praslov, Problems and Theorems in Linear Algebra
(has a long chapter on multilinear algebra and is more readable)
If you are ready for multilinear algebra over a module, try
D. G. Northcutt, Multilinear Algebra, Cambridge U Press, 1984.
Note that this book treats both symmetric and antisymmetric (exterior)
forms in great detail.
Chris Hillman
==============================================================================
From: Janne Pesonen
Newsgroups: sci.math.research
Subject: Re: multilinear algebra sources
Date: Mon, 02 Mar 1998 23:26:57 +0200
ortiz wrote:
> While mathematical litterature on linear algebra abounds in books, few
>
> references are devoted to multilinear algebra (i mean topics like
> tensor
> products, tensor algebra and especially symmetric and exterior
> algebras).
> I was wondering if anyone could recommend some *comprehensive*
> references
> source regarding this matter.
The book by D. Hestenes & G. Sobczyk: "Clifford algebra to Geometric
Calculus" (Reidel, 1984)is very comprehensive source of multilinear
algebra (The chapter 3 is entitled as "Linear and multilinear
functions"). The topics such as tensors, spinors and exterior forms etc
are dealt, along with stuff that is not to be found in any other book
(such as directed integration theory or method of mobiles).
The elementary introduction for multilinear functions is given however
in David Hestenes: "New Foundations for Classical Mechanics" (Reidel,
1986), together with an introduction to geometric algebra with many
applications in classical mechanics, as the title implies.
Regards,
Janne Pesonen, http://fkmarilyn.pc.helsinki.fi/Janne/index.html