Talk:Linear relation

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Text or other creative content from this version of Syzygy was copied or moved into Syzygy (mathematics) with this edit on 1 May 2011. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists.

It seems to me that "Syzygy (mathematics)" is a better title for this page. Mojtabakd «talk» 07:21, 5 October 2021 (UTC)Reply

I disagree. AFAIK, the common use is "linear relation" for individual relations, and "syzygy" is used almost only for the module of all the linear relations, and for relations between relations (2d syzygies). Moreover, for most readers, the current title explains clearly the subject of the article, while "syzygy" is meaningless. Also, it is always better to have a title without disambiguating parentheses, as this allows linking without piping. D.Lazard (talk) 08:29, 5 October 2021 (UTC)Reply

An editor has identified a potential problem with the redirect Stably isomorphic and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 November 8#Stably isomorphic until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Jay 💬 01:21, 23 November 2022 (UTC)Reply

I was curious to know if Cayley explicitly cited astronomy when introducing the term to math, so I looked up Cayley's collected works, and a search for the character string "syz" had only one match. It was the term "syzygetic," and it appeared in the title of a paper by Sylvester that Cayley cited. Does anyone want to take the next step and try to dig up that paper?

-- Greg at Higher Math Help (talk) 16:20, 11 February 2023 (UTC)Reply

Let's say y = M x + c . Do we still call this transformation linear if c ≠ 0 ? Does it matter whether we're dealing with scalars, or a (linear algebra) matrix equation of vectors?

It seems that in some usage contexts, affine transformations in general are deemed not strictly linear. But they do generate straight lines. It might be useful to clarify this.

(Similar question is whether "directly proportional" is the same as "linear", or whether the former implies that the constant of proportionality is positive.)

Cesiumfrog (talk) 12:01, 26 April 2026 (UTC)Reply

AFAIK, a confusion between"linear" and "affine" may occurs only in the case of functions, and this is explained in Linear function. In the case of vectors, matrices, and (geometrical) transformations, "affine" is always when there is a consant term.

"Directly proportional" is used for physical quantities, in physics and statistics and do not applies to functions and mappings. For example, the circumference of a circle is proportional to its diameter, but the image of a vector under a rotation is not proportional to the vector, even if a rotation is a linear map. D.Lazard (talk) 13:27, 26 April 2026 (UTC)Reply