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I have been reading a research paper. The author has used a variable '$x$' with an underline beneath '$x$'. I know that a variable with a line on top of it implies it's arithmetic mean. But I have never seen a symbol with a line under the variable name. Can anyone please tell what it means?

Thanks in advance.

user832788
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sajid
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    You mean $\large{\underline x}$ ? What is the context ? – callculus42 May 16 '16 at 18:16
  • Yes. But the paper is related to Linear Programming. – sajid May 16 '16 at 18:17
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    There is no universal meaning for underlining of variables. It would be impossible to guess the meaning without having the paper identified, but almost surely the author defines that notation before using it. – hardmath May 16 '16 at 18:18
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    "have been reading a research paper" - where? A link would be helpful. Even better, as previously noted, the author surely explained his/her notations somewhere near the paper's beginning. – J. M. ain't a mathematician May 16 '16 at 18:20
  • @user3708999 Can you scan the context and upload? – Narasimham May 16 '16 at 18:27
  • The paper is titled as "ConstantTime Distributed Dominating Set Approximation" by Fabian Kuhn and Roger Wattenhofer – sajid May 16 '16 at 18:30
  • Unfortunately the author did not explain it in the paper. So I thought it must be standard mathematical symbol. – sajid May 16 '16 at 18:31
  • Please edit your question to include that information. I've found a link for you, but you really should have done that yourself. – J. M. ain't a mathematician May 16 '16 at 18:32
  • Underlining was a fairly common way to denote a vector back in the days before LaTeX, because it's easy to do on a typewriter. – Robert Israel May 16 '16 at 18:34
  • @RobertIsrael The article has been published in 2005. – callculus42 May 16 '16 at 18:55
  • True, but old habits persist. You tend to use the notation your professors used, or what you saw in the textbooks. – Robert Israel May 16 '16 at 19:57
  • I don't know about your article, but in one place the authors defined it to be the radical conjugate $$\underline{a+b\sqrt{c}}=a-b\sqrt{c}.$$ This was to distinguish it from the notation for a complex conjugate. The authors also said that this is unconventional. – Favst Jun 24 '20 at 18:18

4 Answers4

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It's not an often-used convention, but in physics, matrices are sometimes appended with a double line underneath and vectors a single line underneath. This somewhat unifies the matrix/vector notation without the clumsiness of vector notation (and how to extend that to matrices).

Cameron Williams
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    Your answer gives me a hint that it should be a vector. It fits in the context. Thanks. – sajid May 16 '16 at 18:27
  • The fact that it's easy to use this notation in handwriting makes it very popular, I think. – Edward Nov 11 '21 at 10:20
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In the article linked below, it seems it is used to mean the minimum possible value of the variable, while the same variable with a line above it means the maximum possible value of the variable.

https://www.researchgate.net/publication/221107546_On_Decision_Making_under_Interval_Uncertainty_A_New_Justification_of_Hurwicz_Optimism-Pessimism_Approach_and_its_Use_in_Group_Decision_Making

mike
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Such a notation often means a vector that is a solution of minimization problem in linear programming.

I googled for another article on MDS problem, it uses just ordinary vector notation (see p.4)

Slowpoke
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My teacher (Statistics) said it is a symbol representing the series of observations$$x_1,x_2,x_3,x_4,\ldots$$in order to reduce space and time.

José Carlos Santos
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TS SARANLAL BK
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