Talk:Invariants of tensors

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[edit] Serious deficiencies

The current (November 12, 2005) version is seriously misleading:

article fails to explain clearly difference between tensors as multilinear operators (concept in multilinear algebra) and tensor fields (concepts of tensor calculus); both individual tensors and tensor fields are said to possess invariants, but these concepts exist at distinct levels of structure,
the terms $I_A, \, II_A$ (first invariant, second invariant, etc.), for the coefficients $a_1, \, a_2$ in the characteristic polynomial

$p_A (\lambda) = \lambda^n - a_1 \, \lambda^{n-1} + a_2 \, \lambda^{n-2} \dots$

of a linear operator (second rank tensor) $A$ is not standard in applied math (or physics); although it may be standard for all I know in some disciplines math usage should trump others, as these are general mathematical concepts useful in many fields,

the coefficients of the characteristic polynomial of a tensor (concept in tensor algebra) are indeed invariants, but they are by no means the only invariants or even the most important ones (see any math book on invariant theory for example, noting that bilinear forms are associated with linear operators and hence a special case of tensors),
the dimension counting argument given in the present version fails for more transformation groups than SO(3), but invariant theory in math/physics certainly deals with many many more groups than this one!

I added a link to an article I wrote which also discusses coefficients of the characteristic polynomial, hopefully successfully informing a wide audience of things which everyone who uses these invariants should probably know.---CH (talk) 23:27, 12 November 2005 (UTC)

P.S. Gosh, is the notation used in this article really standard in some discipline? For heavens sake, profesors of discipline X, stop teaching this horrible notation immediately! CH (talk) 23:39, 12 November 2005 (UTC) (pleading for sanity)

[edit] Engineering application

Can someone please fix the latex math renderings to render every equation. Also, should the last section read "...thus only 3 degrees of freedom..." rather than "...thus only degrees of freedom..."?

Just fixed it. Tomeasy (talk) 10:06, 25 April 2008 (UTC)