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-1
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1answer
74 views

Name of a matrix with one column and row removed [closed]

I am looking for the exact name of a matrix where the i-th column and rows have been removed. I cannot remember how it is called in linear algebra, does anyone got an idea? Thanks!
8
votes
1answer
477 views

Whence “Durchschnitt” and “Vereinigung”?

Today the set-theoretic operations of intersection $\cap$ [German: Durchschnitt] and union $\cup$ [German: Vereinigung] are standard. The modern notations are present in the first edition of van der ...
73
votes
5answers
11k views

Has incorrect notation ever led to a mistaken proof?

In mathematics we introduce many different kinds of notation, and sometimes even a single object or construction can be represented by many different notations. To take two very different examples, ...
0
votes
0answers
41 views

Notations for upward Church-Rosser and upward diamond

The following notations are sometimes used to indicate that a relation $\rightarrow$ is (strongly) confluent: $$ \rightarrow\; \vDash \Diamond; \\ \rightarrow^*\; \vDash \Diamond\ \Leftrightarrow\ \...
1
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0answers
42 views

Question about Notation for Spaces of $n$-ary $k$-ic Forms

Define an $n$-ary $k$-ic form to be a polynomial over the integers of homogeneous degree $k$ in $n$ variables. In Section 1 of the paper "Higher Composition Laws I" (linked below), Bhargava writes $(\...
0
votes
1answer
77 views

Basic question regarding notation of summation over primitive characters

This seems like a very standard notation in analytic number theory, and I see it a lot. But I was confused with it and I would greatly appreciate any clarification. When one writes sum of the shape $$...
-4
votes
1answer
105 views

what does a tildan mean in the context of this math formula [closed]

http://cdn2.hubspot.net/hubfs/2450960/InterviewQuestion_10PAGES.pdf In the above pdf, number 6, bullet 3, contains the following formula: When the classes are unbalanced, the baseline is not 50% ...
5
votes
8answers
2k views

Mathematical objects whose name is a single letter

(Not research-level, but perhaps not easily answered elsewhere — you decide if MO can afford the innocent fun. If so, it should likely be “community-wiki” i.e. one object per answer.) I am seeking ...
4
votes
1answer
172 views

Question about denoting/designating of algebraic structures

I saw this image on Wikipedia (Template:Group-like structures, current revision): Since there are five "properties" that we can have (in this context), namely: totality, associativity, identity, ...
1
vote
1answer
141 views

Notation for the restriction map in Galois cohomology

My coauthors and I are writing a paper based on MO questions and answers: Friedrich Knop's answer, my answer 1 and my answer 2. For a linear algebraic group $G$ over a perfect field $k$, I consider a ...
3
votes
0answers
209 views

Grothendieck construction and coends

In category theory, both the Grothendieck construction and coends are represented by a sort of "integral sign", respectively: $$ \int F $$ for a functor $F:C\to\mathbf{Cat}$, and: $$ \int^x G(x,x) $$ ...
19
votes
5answers
1k views

The letter $\wp$; Name & origin?

Do you think the letter $\wp$ has a name? It may depend on community - the language, region, speciality, etc, so if you don't mind, please be specific about yours. (Mainly I'd like to know the English ...
2
votes
2answers
184 views

Technical term for representing object of a presheaf determined by a left-adjoint?

If $\mathcal{D}$ is a locally-small category, then a functor $F\colon\mathcal{C}\rightarrow\mathcal{D}$ has a right-adjoint if and only if for each object $d$ of $D$, the presheaf $$\mathcal{C}^{\...
2
votes
0answers
214 views

What does the $\pi_1(\mathsf{C})$ really mean?

Assume that $\mathsf{C}$ is a small category (in my case with finitely many objects but this is probably irrelevant). In a paper I'm studying at the moment there is a notion used constantly, this of $\...
3
votes
0answers
502 views

Affine line with a double origin

Is there a standard short notation for the affine line with a double origin $\mathbb{A}^1 \sqcup_{\mathbb{A}^1 \setminus \{0\}} \mathbb{A}^1$? More generally for $X \sqcup_{X \setminus \{p\}} X$ for a ...
2
votes
0answers
54 views

Spectral multiplier and Littlewood-Paley projection

I am trying to understand this paper, and have some basic question, and hope this is OK for the MO. Let $f\in \mathcal{S}(\mathbb R^d)$ (Schwartz Space). We know that $\widehat{\nabla f}(\xi)= 2 \...
3
votes
0answers
108 views

Local system corresponding to induced representation

Let $p\colon Y\to X$ be a finite covering map of path-connected "good" spaces (e.g. manifolds), and let $L$ be a local system on $Y$, and let $V$ be the corresponding representation of $\pi_1(Y)$. ...
5
votes
1answer
295 views

Generalizing Big O notation to arbitrary vector spaces

I'm constructing a Coq library for Big-O notation. Naturally, I'd like it to be as general as possible. The Wikipedia page on Big-O notation says The generalization to functions taking values in ...
6
votes
0answers
193 views

Notation: Why Ω for the based loop functor?

This is just a question about notation - probably useless, but it's always baffled me: Why was $\Omega$ chosen to denote the based loop functor? I once heard someone speculate: "It's because $\Omega$...
-1
votes
1answer
119 views

Typed Values in Formulas

Question: are there any "standard" ways of indicating the meaning of numerical values in formulas, resp. general mathematical texts (theorems, proofs, etc.)? I am especially looking for ...
1
vote
0answers
155 views

Is there standard notation for restriction partial functions?

Given a partial function $f : A \rightarrow B$, and a subset $S \subseteq A$, we get a new partial function $$f \restriction_S : A \rightarrow B$$ by restriction. However, I prefer to analyse $f \...
10
votes
1answer
546 views

History of the pullback corner notation

Where/when did the convention originate of marking pullback (and/or pushout) squares by that little right-angle symbol in the corner? The earliest instance I’ve been able to find is in Paul Taylor’s ...
2
votes
1answer
182 views

Notation for the automorphisms of a $S$-scheme over automorphisms of $S$

Here is a slightly anecdotical notational question. Let $S$ be a scheme and let $X$ be a scheme over $S$, with structural morphism $s\colon X\to S$. Is there a good suggestive notation for the group $...
1
vote
0answers
102 views

Notations - Hardy and Sobolev Spaces [duplicate]

After some confusion on my part, I wanted to know is there a profound mathematical reason why both Hardy spaces and Sobolev spaces are denoted by $H^p$(1). Is it just coincidence? Does it have any ...
7
votes
3answers
269 views

Notations for dual spaces and dual operators

I'm asking for opinions about the 'best' notations for: 1. the algebraic dual of a vector space $X$; 2. the continuous dual of a TVS; 3. the algebraic dual (transpose) of an operator $T$ between ...
1
vote
0answers
112 views

Does the LaTeX $\eqslantless$ symbol, or the comparable Unicode ⋜, have a well defined meaning for binary numerical relationships? [closed]

At first this appeared a simple question; Unicode defines the symbol as "equal to or less-than", which would appear to be the same as "less-than or equal to". But on investigating a bit, I found very ...
4
votes
0answers
125 views

Notation for calculus with measures?

One of the strengths of ordinary multivariable calculus is that you can use notation where functions are expressed pointwise (e.g. $\int_a^b x^2 \, \mathrm{d}x$ rather than merely $\int_a^b f$), and ...
1
vote
1answer
119 views

Using Ordinal Notations in Computability Theory Is There A Standard Notation For The Notations Below $\alpha$

I find I frequently have to refer to the set of ordinal notations below some given notation. For instance given a notation $\alpha$ I often need to refer to the set $\lbrace \beta \mid \beta <^{\...
5
votes
2answers
675 views

What is the standard notation for reversing the order of vector's components? [closed]

If we have a vector $x=(x_1,x_2,\ldots,x_n)$, is there any standard way to denote the vector $(x_n,x_{n-1},\ldots,x_1)$?. I think that $x^{-1}$ could be a good option.
2
votes
1answer
195 views

Stochastic Process Notation

Note: I'm not an expert on stochastic processes. Please use small words and speak real slow. I'm reading a paper [1], which uses a notation for stochastic processes that doesn't seem to be standard. ...
1
vote
1answer
113 views

Notation and reference for polynomials with coefficients not commuting with the indeterminates

Let $R$ be a noncommutative ring (with unit). Then a "fully noncommutative" (for a lack of better wording) monomial over $R$ in the single noncommutative indeterminate $X$ of degree $d$ is given by a ...
11
votes
3answers
829 views

Where does the name “R-matrix” come from?

In quantum integrability and related topics a lot of not-so imaginative terminology is used. One may hear people talk about "Q-operators", "R-matrices", "S-matrices", "T-operators", as well as "L-...
12
votes
5answers
2k views

When did the abuse of notation $y=y(x)$ start?

It's quite common nowadays to name a function and the application of the function to its input with the same letter. (Possibly more so in applied areas. Certainly many calculus textbooks do this.) ...
2
votes
2answers
221 views

Two different kinds of definitions of $C^k(\overline{\Omega})$ — extension and restriction

This is cross-posted in MSE. I have seen two different kinds of definitions of the notation $C^k(\overline{\Omega})$ — by "extension" of functions on $\Omega$ or by "restriction" of functions on $\...
4
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0answers
118 views

Pairing in Group Cohomology [closed]

I am following Ararat Babakhanian's Cohomological Methods in Group theory. Let $A,B,C$ be $G$ modules then we have a $G$ module structre on $\text{Hom}_{\mathbb{Z}}(B,C)$ with $$\sigma.f(x)=\sigma(f\...
1
vote
0answers
54 views

Notation for largest universal subclass and class of arrows “locally in” a given class of arrows

Let $\mathcal M$ be a class of arrows in a category $\mathsf C$. I would like suggestions for good notation for the following two classes. The smallest universal (pullback stable) subclass $\mathcal ...
0
votes
1answer
68 views

Theory of integration of Kernel in çinlar probability and stochastic

I'm reading the probabilistic book write by çinlar, but I don't understand the Kernel theory, in details: $ (E,\mathcal{E}),(F,\mathcal{F})$ are two measurable space $$K:E \times \mathcal{F} \...
4
votes
1answer
255 views

What countable ordinals are called $\kappa_\alpha$?

Jervell has a notation for countable ordinals up to the small Veblen ordinal using trees: • Herman Ruge Jervell, How to wellorder finite trees and get good ordinal notations, Berkeley Logic ...
4
votes
0answers
98 views

Is there a name for groups of the form $Sp(1)^n$?

A (compact) torus is a Lie group isomorphic to the product of finitely many circles: $T^n = S^1 \times \cdots \times S^1$. Such groups are extremely important in Lie theory, Differential Geometry, ...
12
votes
3answers
1k views

History of the notation for substitution

One of the very common notations for syntactic substitution is $[\ /\ ]$. However, there seems to be an inconsistency in the literature about its usage. Many write $[t/x]$ for "substitute $t$ for $x$...
1
vote
0answers
134 views

Name for the Quotient $SU(m+1)/(SU(k) \times SU(m-k))$

The sphere $S^{2m-1} \simeq SU(m+1)/SU(m)$ has a canonical $U(1)$-action, and quotienting by this action give complex projective space $CP^m$. We can generalise the family of sphere to the family of ...
0
votes
0answers
221 views

Notation for iterated summation

Is there a more compact way to write $$ \sum_{i_1=0}^{N} \sum_{i_2=0}^{N-i_1} \sum_{i_3=0}^{N-i_1-i_2} \cdots \sum_{i_{K}=0}^{N-i_1-i_2-i_3-\ldots-i_{K-1}} a_{i_1i_2i_3\ldots i_K} $$ as something like ...
0
votes
2answers
355 views

Use of ternary operator in formal writing

I would like to write $$ f(x) = \begin{cases}1&\mbox{if }x = 1\\ 0&\mbox{otherwise.}\end{cases} $$ However, this eats up a lot of vertical space for a very simple statement. Is there agreed ...
0
votes
1answer
95 views

Comparing vectors with numbers? [closed]

My question pertains to the paper "A Simplified Proof of the Divergence Theorem" by Djairo Guedes de Figueiredo. It's not a big question, actually, but it's confusing me a lot: In the statement of ...
1
vote
0answers
30 views

Notation to denote substitution of vector elements [duplicate]

I'm looking for notation to denote vector substitution and elimination of elements. This is possible using set notation, but I am looking for shorthand notation that is perhaps already in use. ...
1
vote
0answers
89 views

Notation clash between a representation and spectral radius

I am currently writing a paper where I need talk both about a representation of a semisimple Lie group (usually denoted by $\rho$), and about spectral radii of linear maps (also usually denoted by $\...
2
votes
0answers
87 views

What does the square root sign tells us in the wave equation? [closed]

I have been reading the paper on wave equations, and I have some confusion in notations. Consider the initial value problem(IVP)(Wave equation): $\frac{\partial ^2 u } {\partial t^2}(x,t) = \...
-2
votes
1answer
282 views

Correction symbols used for mathematical texts [closed]

When proof reading and correcting a mathematical text, I sometimes see people use special notation symbols in the margin to indicate correction, deletion, replacement and so on. Is there any standard ...
7
votes
1answer
340 views

What does the notation $[b_1,b_2]$ in M. Hochster's “Prime Ideal Structure in Commutative Rings” mean?

I'm reading the article M. Hochster, Prime ideal structure in commutative rings, Trans. Amer. Math. Soc. 142 (1969), 43--60. Freely available here on the journal's website. But, I can not find the ...
3
votes
1answer
157 views

What is the function space $H^1_{m, \sigma}$?

I am reading Hildebrandt's and Widman's 1975 paper on "Some regularity results of quasilinear elliptic systems of second order". Theorem 3.1 is the first time in their paper that the function space $...