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Similar to "FORTRAN or Fortran?", I've seen the Mathworks produced software package written as MATLAB (for example, see this Wikipedia article, and the product web site) and also as Matlab (for example, see this article on an toolbox put out by MIT's Lincoln Lab). Are we establishing a convention here, and if so, what convention?

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As it's a registered trademark of the Mathworks, I'd go with their capitalization: MATLAB.

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    $\begingroup$ Agreed. It's how Cleve Moler originally wrote it; it's how MathWorks writes it. I see no arguments against going with their preference... $\endgroup$ – J. M. Jan 15 '12 at 10:42
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This question puzzled me. So I dug a bit around.

TL;DR

Matlab seems like a much better choice for a non-legal document. For example, a journal paper or a SE community answer. Unless such spelling explicitly contradicts the style guide of the publication you are writing for.

However, I would avoid "Matlab®" for multiple reasons.


Motivation for Matlab vs MATLAB[®]

  • The trademarked term is usually treated as a proper noun, which implies capitalization; however, not all-caps, but title caps.
  • As far as I understand, the US copyright law requires the treatment as a proper noun but does not require to replicate all the stylistic details, which would include all-caps.

I am a bit shaky on presenting the actual excerpt from the legal document here.

Audience for This Guide

The brand guide is for MathWorks distributors, external creative contractors, and agencies who create MathWorks materials.

Nothing here dictates me, a person who is not affiliated with MathWorks, to be obliged in using their view on appropriate capitalizations.

Particular style guide examples:

When deciding how to format a trademark, editors should examine styles already in use by independent reliable sources. From among those, choose the style that most closely resembles standard English – regardless of the preference of the trademark owner. Do not invent new styles that are not used by independent reliable sources.

In general, discourage capitalization in text except where absolutely necessary.

...

The trademark symbols ™ and ® are no longer used. Capitalize the first letter in the trademark name only.

Sources:

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I support writing "Matlab", with just one capital letter. This is the normal English capitalization rule. Abusing capitalization and special characters for emphasis is just a commercial trick, but I don't think it has any advantage when it comes to legibility.

See this Washington Post copy editor's take on the topic.

  1. Everything you need to know about capitalization you learned in kindergarten.

Well, that might be an exaggeration, but the point is that the most basic of capitalization rules are not to be trifled with. Proper nouns are capitalized. All caps is for initial-based abbreviations. [...]

  1. Funky logos are nothing new.

In the old days, battles on this front usually involved companies that insisted on being identified in all caps. The uppercase treatment, after all, makes something STAND OUT. But there weren't as many battles as there are today, because copy editors and even writers knew that logos are logos and English is English. "You want all caps?" an ink-stained wretch with a green eyeshade might have asked. "Go buy an ad!"

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  • $\begingroup$ I do not think that this follows capitalization rules, since a stylization matter. $\endgroup$ – nicoguaro Apr 30 '19 at 18:08

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