Talk:Hyperdeterminant

Expansion

I plan to expand this article shortly to cover general properties of hyperdeterminants, their history and applications. Any suggestions regarding the content so far is welcome. Weburbia (talk) 21:10, 24 January 2008 (UTC)

Error

"This expression acts as a discriminant in the sense that it is zero if and only if there is a non-zero solution in six unknowns xi, yi, zi, (with superscript i = 0 or 1) of the following system of equations "

I think there's a small inaccuracy: It should say "if and only if there is a non-trivial solution". Indeed, the generic system has non zero solutions. It's a subtlety but it seems more complicated to check. As a counter-example consider the tensor defined by $a_{000}=a_{111}=1$ and $a_{ijk}=0$ for $ijk\neq 000,111$. In that case, the definition gives $Det=1$ but the system becomes $x_{0}y_{0}=x_{1}y_{1}=x_{0}z_{0}=x_{1}z_{1}=y_{0}z_{0}=y_{1}z_{1}=0$ and admits $x_{0}=x_{1}=y_{0}=y_{1}=0$, $z_{0}=z_{1}=1$ as a solution.

A non-trivial solution means that the solution can not be obtained by specializing the solution of the system for generic values of the parameters.

jglJgluque (talk) 16:03, 21 August 2018 (UTC)

Hi jgl,

I agree with you that there is an error here. Is it equivalent to your suggestion to ask for a solution in which none of the vectors $(x_{i}),(y_{i}),(z_{i})$ is zero? Separately, do you have any idea if there is a published source (journal article or book, for example) that supports the correction?

Thanks, JBL (talk) 16:00, 22 August 2018 (UTC)

Hi JBL

Yes, but I don't know if it is easy to prove it directly without the help of algebraic geometry.

The property can be found in the book of Gelfand, Kapranov and Zelivinsky p445.

best

Jgluque (talk) 17:07, 22 August 2018 (UTC) Jgluque

Thin spaces

@Joel Brennan: Greetings, and thanks for your work on this and other math articles! Regarding this revert, I guess I should explain that I'm working off an automatically prepared list of characters disfavored by the Wikipedia Manual of Style and HTML entities that can be converted to make wikitext easier to read for editors. For whitespace, we're not supposed to use raw characters for anything other than a standard space (" ") to avoid confusion. For thin spaces, {{thinsp}} is available (and won't show up on my reports) if absolutely necessary, and the general idea is that wikitext is easier to use than HTML (especially somewhat obscure syntax like this).

Another consideration is the directive of MOS:MARKUP to "keep markup simple". Sometimes this involves sacrificing some typographical sophistication, and precise control of whitespace seems to be one of the things we disfavor in most situations compared to streamlined markup. That's why I often remove thin spaces or replace them with regular spaces. In this case, it seems removing the space completely was the wrong choice. I looked into the preferred whitespace treatment for "×", and found that Wikipedia:Manual of Style/Mathematics#Multiplication sign uses regular spaces on both sides. This makes sense; in my web browser (Firefox on Linux) I don't actually see much difference in appearance between 2 × 2 × 2 and 2 × 2 × 2, but {{nowrap|2 × 2 × 2}} is a lot easier to read than {{nowrap|2{{thinsp}}×{{thinsp}}2{{thinsp}}×{{thinsp}}2}}. So, I propose changing those thin spaces to regular spaces. Does that make sense? -- Beland (talk) 03:39, 22 February 2022 (UTC)

@Beland: Yes that all makes sense. I will admit that I use thin spaces quite liberally in my edits and some of them are probably not necessary, but if I had to choose one instance where it improves the aesthetics of the text it would be this one (dimensions of matrices/arrays) – perhaps the effects are browser dependent, but in my browser (Chrome on Linux) "an m × n matrix" looks much better than "an m × n matrix" or "an m×n matrix", and moreover "{{thinsp}}×{{thinsp}}" hardly obscures or complicates the markup at all* in comparison to other uses of thinsp; or nbsp; (e.g. when someone uses a nbsp; for every space in a formula rather than just enclosing it in <nowrap></nowrap>). Therefore for this article (where this usage of {{thinsp}}×{{thinsp}} is very frequent) I would urge that the spacing remains as it is, although you are welcome to change the "thinsp;"s to "{{thinsp}}"s if it matters to you. By the way, can I ask what the non-HTML equivalent of nbsp; is, or would this just be <nowrap></nowrap>?

*99.9% of the time one is dealing with matrices as opposed to hypermatrices / higher-dimensional arrays, so only two thin spaces are needed as opposed to longer chains like {{nowrap|''n''{{thinsp}}×{{thinsp}}''n''{{thinsp}}×...×{{thinsp}}''n''}}

Joel Brennan (talk) 21:46, 22 February 2022 (UTC)

@Joel Brennan: Yes, using &nbsp; certainly makes formulas hard to read, and where I see this I convert them to use {{nowrap}} (or {{math}} if there is <math>...</math> markup in the same article). The point of having an MOS is that the decisions made there apply to all articles, so the project has consistent typography, and editors of individual pages can quickly settle differences of opinion by looking at the site-wide consensus. No matter what choices are made by the MOS, some individual editors will have different preferences, but consistency is generally held to be more important than what is often a somewhat arbitrary and unimportant choice. Whether I think thin or regular spaces look better here, I think it's more important to follow the style the MOS clearly uses, which in this case is regular spaces. -- Beland (talk) 07:52, 27 February 2022 (UTC)