[112] in mathematical software users group
Tensor algebra question - well, sort of
daemon@ATHENA.MIT.EDU (Reid M. Pinchback)
Thu Oct 28 11:37:42 1993
To: msug@MIT.EDU
Date: Thu, 28 Oct 93 11:35:41 EDT
From: "Reid M. Pinchback" <reidmp@MIT.EDU>
Ok folks, I've got an oddball question that I've been scratching my
head over the last month or two. It first came up when I was toying
with ways of improving the 'evalm' matrix-expression evaluator
in Maple.
Not having much of a background in physics, I've often wondered what
tensors are all about. Curiosity finally got the better of me, and I
decided to find out. Having wandered through assorted linear algebra
and tensor texts, I've run into a point of confusion.
Just what is the underlying algebra for tensor-like manipulations?
Everything I've read about tensors has always been presented in the
context of the usual miasma of multivariate calculus and differential
geometry needed for physics and engineering applications. This would be
like always presenting linear algebra in the context of second-year
undergrad vector calculus, and thus obscuring the fact that linear algebra
is simpler and more general than this particular application of it. As a
result, as I keep digging into tensors I keep running into questions that
tend to boil down to trying to figure out if some manipulation or definition
is used because of the (obscured) algebraic properties involved, or because
of the needs of the calculus wrapped around the algebra. In other words,
it appears that tensors = {calculus,analysis,diff. geometry} + algebra X,
where algebra X is something other than (and probably more structured than)
ordinary linear algebra. What is X?
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Reid M. Pinchback
Faculty Liaison
Academic Computing Services, MIT
