# Tagged Questions

Question on the meaning, history, and usage of mathematical symbols and notation. Please remember to mention where (book, paper, webpage, etc.) you encountered any mathematical notation you are asking about.

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### Exponential of adjoint action notation confusion

I'm getting a bit confused about the notation with the exponential map and the adjoint action. Could someone explain to me what $$\text{exp}(t\text{ } ad(X))(Y)$$ means, where $X,Y$ are both ...
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### How to express in an equation, a constant plus a random sample?

Suppose I have a Beta distribution, and want to express in an equation a random sample from this distribution. I could say $x \sim Beta(\alpha, \beta)$. Now, consider the case when $x$ is a constant ...
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### $24\otimes 24$ notation for representations of $SO(24)$

I was working through a set of string theory notes, and I came across the notation $24 \otimes 24$ to denote a reducible representation of $SO(24)$, but I am not familiar with the notation. I have ...
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### An indices-like notation for the adjoint matrix

Looking for a way to define a specific element in the adjoint matrix of a known nxn matrix, using an indices-like notation, which is not depended on the matrix minors or cofactor matrix. (Maybe ...
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In what Structure point addition is not allowed and that makes points different from vectors.I mean in any Field or even Group i can add without problem but i have seen people saying point addition ...
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### What is the meaning of the subscript sometimes seen after Cartesian products in geometry?

I often seen a subscript after a Cartesian product, e.g. $A \times_\kappa B$, for example in this Wikipedia article about the spin bundle. What is the meaning of this generalised Cartesian product? ...
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### Project a Sequence on a Set

I am reading this paper and looking at Section 2.1: If $\sigma$ is a sequence over $K$ and $L \subseteq K$, then $\sigma \lceil L$ denotes the sequence obtained by projecting $\sigma$ on $L$. What ...
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### When denoting a utility function in terms of real numbers R, what does the plus in subscript denote?

So, we can see that for the below question, we are asked to show linear demand for a utility function $(\mathbb{R}^n)_+ \to \mathbb{R}$. My question is, what does the plus symbol in the set R ...
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### Notation Question - Indicating Asymptotic Values

How would you mathematically indicate a value "right next to" another value For example, the value "just before 4" is $4-.0000...1$, right? Or the theoretical minimum $Y$ value of y=2^x is ...
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### McDougall Litell Issues with notation

My school uses textbooks by a company called McDougall Litell for all math classes. My friend pointed out to me that there was no really decent notation used in any of those books. Would it be ...
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### Reference request for a notation stating absolute error

My Question: Let $\Delta(a_n)$ be defined by $$(a_n)\in \Delta(a_n)\iff \forall n\in\mathbb N: |\epsilon_n| \le |a_n|$$ I guess it is very likely that this notation is already used in mathematical ...
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### Vector Calculus Notation for “Gradient of a Vector”

Given (differentiable) functions $\,n_{1,2}:\mathbb{R}\to\mathbb{R}\,$ we write vector $\renewcommand{\arraystretch}{2}$ \begin{align} \vec{\boldsymbol{n}} = \begin{bmatrix} n_{1} \\ n_{2} ...
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### Best practice for naming variables to distinguish chosen upper bound from computed maximum.

Say I have a vector of a matrix's singular values $[s_1, s_2, \cdots, s_N]$, and would like to define two variables, one which holds the maximum value in the vector, and another which holds an ...
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### Is there a more concise way to indicate many elements that belong to a set?

In the article I'm writing I faced the following situation: ∀a∈A, ∀b∈B, ∀c∈C, ∀d∈D, ∀e∈E, ∀f∈F, ∀g∈G, ∀h∈H, ∀i∈I, ∀j∈J, ∀k∈K, ∀l∈L I end up having to write that line lots of time and this is making ...
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### Minimum Index of a Sequence given a certain condition

Let $S = \langle 1,3,5,8,13 \rangle$ be a sequence. Whicho notation could I use to denote the "minimum position of $S$ where $s_k \geq 5$? In this example, the function would return 3 (the position ...
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### Notation: What does $[0,1]^2 \backslash [0,0.5]^2$ mean?

The context of the of the problem is computing a integral in two variables. So I guess: $[0,1]^2 \backslash [0,0.5]^2 = (0.5,1] \times (0.5,1]$ But I wonder, why one has just not written the latter ...
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### What is the name of $E_n[x]$ ?!

I am writing a paper, I want to introduce the $E_n[x]$ Is it correct to write: $E_n[x]$ represents exponential integral of order of n I know $E_i[x]$ or $E_1[x]$ is called exponential integral. ...
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### About random variable and probability notation

I'm reading material about Markov chain and confused with notation of probabilities (probably something more than notation). Could anyone explain the difference between these notations, please. Given ...
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### First Matching Sequence

Let $Q = \langle a,a,b,a,b,b \rangle$, $R = \langle a,a,a,b,a,b,b \rangle$ and $S = \langle b,b,a,a,b,b,b,a \rangle$ be sequences. If two elemens are equal, they are said to match (e.g., ...
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### Meaning of the notation $\langle X\rangle$

What does the <> enclosing the Xj in the following equation mean? Do I just treat them like ordinary parenthesis or does ...
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### Is there a word to say that a vector takes the size such that the matrix notation makes sense?

I am handling with a vector, lets call it $\iota$ which should describe a vector of ones. While writing a text I realized that it is somewhat cumbersome to include a subscript describing its length, ...
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### asin, arcsin, $\sin^{-1}$ - is there any convention?

I've seen multiple forms how the arc sine is marked. But is there any convention which form is mostly being used? Does this depend on the country?
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### What is a good language to represent a mathematical formulas as code

What is a good language to represent a mathematical formulas as code? I am interested in representing my math formulas in various documents so that they can easily implemented in various programming ...
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### Why aren't square roots written between vertical bars (absolute value)?

The root of a number $x$ is $y$ and $-y$. So why aren't we writing either $|\sqrt{x}|$ or just $\sqrt{x}$ to determine if someone wants $-x$ or $x$?
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### Notation troubles: What is $\hat{C}(I)$ for Ethier and Kurtz 1986?

One finds in Ethier Kurtz 1986 (page 367) I couldn't find a definition on the book (It is a large book, and I found no table of frequently used notations) What is $\hat{C}(I)$?
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### n-tuples notation confusion

I am slightly confused with Cox, Little, O'Shea's Ideals, Varieties and Algorithms. So, it talks about $n$-tuples $\alpha = (a_1,a_2,...,a_n) \in k^n$ where $k$ denotes a field. So, when I wish to ...
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### Superscript in Probability notation

What does it mean when you write $P^2(A)$? If it's just a square, why not just write ${P(A)}^2$ or $(P(A))^2$?
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### Triangle groups: reflection notation

Consider a triangle group $(a, b, c)$. I'm wondering if there's a standard notation to describe traversing triangles in the tiling by reflection? Example: given a certain starting triangle on the ...
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### How to represent this matlab code in mathematical notation?

I have this code in matlab: z = linspace(d1,d2,n)*W/t; I am wondering how to express this operation in mathematical notation? I was thinking of something like ...
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### double horizontal bars notation for sets

I am unsure of the meaning of a specific notation. We have a two-dimansional matrix $I_B$ (representing an image after applying Gaussian blurring to it, but that's just background information). Let ...
In index notation, does the term $σ_{ik}x_{j}n_{k}$ mean $\bf{σx}\cdot\bf{n}$ or $\bf{xσ}\cdot\bf{n}$? Here $σ$ is a second-order tensor and $x,n$ are vectors. On the same note, is ...