Talk:Tensor (intrinsic definition)

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I am now trying to make this page more easily maintainable, by replacing Wiki markup + Unicode with TeX markup for the math stuff. This makes this page visible in many more browsers, and should make the page more editable for experts; of which I am not one. Could any mathematicians here proof-read this article, please?

Can I protest (a) about calling things in mathematics 'formalisms' (which is too much like Serge Lang for me) - one might as well say 'unmotivated stuff'; and (b) calling things 'modern' - unlike calling things classical, which is fair enough?

Charles Matthews 09:11, 12 Nov 2003 (UTC)

Charles, what name would be suitable?

• Tensor (differential geometry treatment) ?
• Tensor (component-free treatment) ?
• something else?

-- The Anome 22:44, 12 Nov 2003 (UTC)

Tensor (abstract algebra) is good. The old argument (six decades ago now) was: don't say modern algebra (perishable), say abstract algebra. In fact there is an argument now to go further to tensor (category theory) (as well, not instead of) for monoidal categories.

Charles Matthews 17:55, 13 Nov 2003 (UTC)

Tensor (differential geometry) is better, except that even the component-treatment is differential geometry... I don't quite think abstract algebra covers tensor bundles, differential manifolds, connections, sections, etc... Phys 17:25, 14 Nov 2003 (UTC)

Connections? Keep on topic, please. This is the old argument (for tensors here) that you have to introduce tensor fields at the same time as tensors. Why? There is a page for tensor fields.

Charles Matthews 18:50, 14 Nov 2003 (UTC)

I've looked around a bit - not hard to find ten 'tensor' pages. I think this tells me something a little more positive, namely that this isn't really a name-space problem any more. It's more a question of licking the hypertext into shape. I've not moved any pages up to now, and don't intend to start.

Charles Matthews 20:17, 14 Nov 2003 (UTC)

Wow, this page has mobilized! What is intrinsic definition supposed to mean? aren't tensors in general intrinsic definitions of a space? isn't that what riemannian geometry (classical tensors) is known for: intrinsic definition of curvature? how else would one use the phrase "intrinsic definition" other than refering to the topology of the space or curve? does one mean by this "component-free"? if so, why not just say "component-free" instead of the ambiguous, mysterious, and confusing (because of its allusion to the intrinisic definition of curvature in riemannian geometry (classical tensors)) "intrinsic definition".

regarding "abstract algebra": (and someone mentioned differential geometry) there was discusion earlier in the Talk:Tensor page regarding the topical arrangement of the mathematics page, and where in that tensors should go (why they are on top), and it was concluded that they belong in both the abstract algebra section (for the modern treatment) and the differential geometry section (for the classical treatment), which makes a lot of sense. maybe "abstract algebra approach" would be more fitting, informative, and helpfull, seeing that the approach is based on abstract algebra, comes from the perspective of abstract algebra, and one needs to know abstract algebra in order to learn it.

--Kevin Baas Still suggesting:

• Tensor (absract algebra treatment)

-- Kevin Baas 14:41, 24 Feb 2004 (UTC)

This article needs re-hauling. The title is inadequate and suggests confusion with the notion of tensor fields in differential geometry. The header, as others have above suggested, ought to be: "Tensors (algebraic treatment)". While listing the correct properties of a tensor space, the standard explicit construction (in terms of a quotient of some free module) is not provided. Tensor products from the viewpoint of category theory (as covariant functors) should at least be briefly hinted at.

--Anon 14 July 2006.

[edit] discussion at Wikipedia talk:WikiProject Mathematics/related articles

This article is part of a series of closely related articles for which I would like to clarify the interrelations. Please contribute your ideas at Wikipedia talk:WikiProject Mathematics/related articles. --MarSch 14:11, 12 Jun 2005 (UTC)