Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

learn more… | top users | synonyms (2)

19
votes
4answers
1k views

Is there anything special about this matrix?

I've just encountered a matrix which seems to display nothing special to me: $$B=\begin{pmatrix}1&4&2\\0 &-3 &-2\\ 0 &4 &3 \end{pmatrix}$$ But further observation reveals ...
1
vote
0answers
30 views

Does this PDE have a name? $y u_{xx} + u_{yy} = 0$

I am asked to solve the following equation: $$y u_{xx} + u_{yy} = 0, \quad -\infty < x < \infty, \quad y > 0, $$ together with $u(x,0) = \cos{qx}$ and bounded solution when $y \to \infty$. ...
2
votes
2answers
39 views

Linear algebra terminology: unique, trivial, non-trivial, inconsistent and consistent

Let me get this straight: Unique solution- has an exact solution (such as a POI of 2 intersecting lines) Trivial solution- when 0 needs to equal the zero vector in $Ax=0 vector$ Non-Trivial-? ...
2
votes
2answers
148 views

Why did they need to say that the image is a subset?

I'm reading the course notes on rings at the moment, but noticed something that didn't quite make sense immediately to me. Suppose $R$ is a ring and $f : R \to S$ is a homomorphism. Let $T = ...
0
votes
1answer
34 views

Is this alternate definition of Limit correct?

Would it be correct to define the limit of a series as the smallest number that no number in the series is greater than (for an increasing series, the other way around for a decreasing series, i.e the ...
0
votes
1answer
39 views

change the order of the digits of a prime number

What is prime numbers called, that if you arbitrary change the order of its digits, you will only get another prime number. For example 79 (79 is prime number as well 97) or 199 (199, 919, 991 is ...
4
votes
1answer
154 views

What is the difference between Calculus and Analysis? In Stochastic processes?

I guess one could say that Calculus is just a non-rigorous version of Analysis. What about in subjects involving stochastic processes? I took up masteral classes called stochastic calculus. I plan to ...
1
vote
1answer
35 views

Modifying the Peano Axioms to allow multiple successors

If you took the familiar Peano Axioms and replaced the axiom $x \in \mathbb{N} \implies \exists y\in \mathbb{N}(y =S(x))$ with $x \in \mathbb{M} \implies (\exists y_1\in \mathbb{M})(\exists ...
1
vote
3answers
82 views

What is the name of a number ending with zero's?

I am currently writing a very specific graph of a function implementation. The graph can have min/max values e.g. $134$ and $1876$ respectively. I'm calculating "nice" numbers. For min/max they are ...
5
votes
1answer
232 views

What does “hom” stand for in hom-sets and hom-functors?

With given category $\mathcal{C}$ and its objects $A$ and $B$, a hom-set $\hom_\mathcal{C}(A, B)$ is the collection of all morphisms from $A$ to $B$. There is also a related notion of hom-functor ...
1
vote
1answer
43 views

Term for relationship of set overlap without containment?

What is the term for the relationship between two sets that share at least one common element, but neither set is a proper or improper subset of the other? $$ A?B=_{def}\exists x \exists y \exists z ...
0
votes
0answers
12 views

Name of $\bar{F_E}$?

Let $E/F$ be a field extension. Define $\bar{F_E}:=\{\alpha\in E : \alpha \text{ is algebraic over } F\}$. What is the standard name of this? Fraleigh calls it 'the algebraic closure of $F$ in ...
9
votes
2answers
151 views

Is there a term for two polygons with the same angles but different side lengths?

Suppose polygons $A$ and $B$ have the same number of sides, and there is a correspondence between the vertices of $A$ and $B$, in consecutive order around both polygons, so that the angles at ...
2
votes
1answer
82 views

What is the difference between Boolean logic and propositional logic?

As far as I can see, they only employ different symbols but they operate in the same way. Am I missing something? I wanted to write "Boolean logic" in the tag box but a message came up saying that if ...
4
votes
0answers
75 views

In the mean value theorem, we are guaranteed $c$ such that $f'(c) = (f(b)-f(a))/(b-a)$. Does $c$ have a name?

The Mean Value Theorem says approximately that for differentiable $f$, there is a $c \in (a,b)$ such that $$ f'(c) = \frac{f(b)-f(a)}{b - a}. $$ I presume that the number $f'(c)$ is the mean value. My ...
1
vote
0answers
29 views

Terminology: Opposite of “refinement”

Let A be a partition of a set, and B a refinement of A. Fill in the blanks: A is a __________ of B. I know that A is coarser than B, but how does one turn that into a noun?
2
votes
1answer
21 views

Is there a term for “mutually define”?

Today, I learnt about the relation between inner product space and normed space which parallelogram law holds. Then I had wondered about something like this: Let $A$, $B$ are 2 types of structures. ...
4
votes
1answer
40 views

What is the name for a rectangular figure of many sides?

What is a polygon where each edge is at a 90 degree or 270 degree angle to the prior edge (giving both concave and convex vertices) called? Here is one example of such a shape: ...
0
votes
2answers
38 views

Simple Explanation of Geometric distribution?

I really understood the explanation of Hypergeometric distribution by looking at this answer but when it comes to Geometric distribution I can't get how they calculate the probability distribution of ...
0
votes
1answer
24 views

More explicitly, what is $\left(p_n\right)_{n\in\mathbb{Z}}$ in this paper's context

I'm reading this paper and on page 3 between just prior to their mentioning of $\left(2\right)$ they state the following: ...if there is a sequence of polynomials ...
2
votes
0answers
26 views

Terminology for subsequences?

Note: I'll index all my sequences by $\mathbb N$, so I drop the indices in the sequence notation. The notion of a subsequence of a sequence $\{a_n\}$ is a sequence obtained by deleting some terms in ...
0
votes
0answers
17 views

“Branch” of a correspondence

I just saw for the first time references to the "branches" of a correspondence. Examples of the use of the terminology can be found in ...
3
votes
2answers
42 views

Function with an $x$ not in simple form

I've stumbled upon a practice example in an old textbook which I find confusing. Maybe it's because I haven't reached part of an explanation yet (went through pages, haven't found anything of help). ...
0
votes
0answers
15 views

Formally correct “generator expression” for parameters of a function

I'm trying to express formally correct that a class of functions exists that have a certain property that applies to all concrete "instances" of this class. In that I try to write a "generator ...
2
votes
0answers
28 views

Invariant subspace vs. irreducible subspace (terminology)

In a course in representation theory I was presented the following proposition: Let $(\pi,V)$ be a finite dimensional irreducible representation with a cyclic vector. $V$ has a unique max. proper ...
1
vote
0answers
29 views

Definition - limit of a sequence - uses “rank”?

I have the following definition in my book, and was confused as to the context of the word "rank" here. The definition is as follows: A sequence $(u_n)_{n∈N}$ has limit $l ∈ R$ as $n → ∞$ (we also ...
2
votes
2answers
123 views

What is the phonetic way to say $10^{99}$

More specifically, $10^6$ is one million, $10^9$ is one billion. So what is $10^{99}$?
3
votes
3answers
475 views

Is there Mathematical discipline that treats mathematical logic, axioms and relations as one big mathematical object?

Recently I was self studying the properties of the Wronskian $W$ using various lecture notes and Wikipedia I knew that if $W\ne0$ for at least one x then the functions are linearly independent I ...
0
votes
3answers
128 views

What is the branch of mathematics that combines discrete mathematics and linear algebra known as?

Many different branches of mathematics are combined together. For example, algebra and topology combine to give Algebraic Topology; algebra and geometry give rise to Algebraic Geometry, etc. What is ...
1
vote
2answers
38 views

The ambiguity of the meaning of the term “average”

Suppose $\{x_1, x_2, \ldots , x_n\}$ is a set of data of n weights. The average weight is then (the sum of these weights divided by $n$), right? Now, suppose $\{x_1, x_2, \ldots , x_n\}$ is a set of ...
1
vote
1answer
38 views

What's the name of the sequence of differences?

Let $a = (a_0,a_1,a_2,\ldots)$ be an infinite sequence of real numbers. What is the name of the sequence \begin{equation*} Da = (a_1 - a_0, a_2 - a_1, a_3 - a_2, \ldots) \qquad ? \end{equation*} ...
0
votes
0answers
35 views

What do we call $R$-bilinear maps $V,W \rightarrow R$?

Let $R$ denote a fixed commutative ring. Then given an $m \times n$ matrix $A$ with entries in $R$, we get an $R$-linear transform $R^n \rightarrow R^m$ in the usual way. We also get an $R$-bilinear ...
0
votes
0answers
18 views

Term for the product of the coordinates of a position vector?

Suppose I have a position vector $v$ and I multiply its $x$-component by its $y$-component to get the product $p$. Is there a single term to describe $p$?
1
vote
0answers
18 views

What is a dominating measure?

When I read papers in statistics, I meet the notion of "dominating measure", can anyone explain this notion to me a little bit ? Thanks
0
votes
1answer
44 views

Are fixed points and equilibria the same thing?

Are fixed points and equilibria the same thing, in terms of a logistic map?
2
votes
0answers
28 views

Unique Union Problem

Given a the set $a = \{1,...,n\}$ and let $b$ denote a set of subsets of $a$. Find a subset of $c$ of $b$ so that the union of all subsets in $c$ is equal to $a$ and the intersection of any of the ...
2
votes
2answers
40 views

How is the start of repeating decimals defined?

Today I tried to find the period length of the repeating decimals of 8/86 by asking WolframAlpha (yes a somewhat stupid question because it's the same as ...
2
votes
5answers
219 views

What does $\prod_{k=-2}^{11}(15-3k)$ mean--and how might I compute it?

$$\prod_{k=-2}^{11}(15-3k)=\;?$$ I'm new to this and have not seen this notation before. Can anyone explain to me what this is called and how to solve or compute it?
0
votes
0answers
24 views

Universal property of tensor product of $R$-algebras

Let $R$ be a commutative ring and $A_1,...,A_{n+1}$ be $R$-algebras. Let $A_1\otimes_R\cdots\otimes_R A_{n+1}$ be equipped with the natural $R$-algebra structure. Let $N$ be an $R$-algebra. Let ...
1
vote
0answers
38 views

Name of this PDE: $\frac{\partial^2u}{\partial t^2}=\frac{\partial^3u}{\partial x^3}$

So I got an exercise to try some numerical methods on the following PDE: $$\frac{\partial^2u}{\partial t^2}=\frac{\partial^3u}{\partial x^3}$$ I tried to find some information about it, but I do not ...
1
vote
1answer
23 views

Why there is a less care of symmetricity of bimodules over a commutative ring?

Let $R$ be a commutative ring. Then, we say $M$ is an $R$-module instead of left $R$-module or right $R$-module or $(R,R)$-bimodule. I'm curious why this convention is acceptable in general. Let's ...
0
votes
0answers
26 views

Understanding what paths,trails and circuits and cycles and walk length mean

My Research I've looked at two questions which seemed similar on MSE. The first one was inadequate for me because most of the answers where just stating book definitions, which I already have. The ...
2
votes
1answer
47 views

How to call “equivalent-looking” vertices in graph..?

In the above figure, the vertices expressed as blue dots are "equivalent-looking." Although my expression is somewhat ambiguous, I believe one can simply answer it. How can we call such vertices? ...
0
votes
0answers
15 views

The terminology of the operation in the linear function

What do we call the term $(m_0 + m_1 \times x_1 + m_2 \times x_2)$ in the linear equation $f_\vec{m}(\vec{x}) = m_0 + m_1 \times x_1 + m_2 \times x_2$? is it correct to call it the linear combination? ...
0
votes
1answer
42 views

How do geometers define “locally looks like” in differential geometry?

From reading some introductory texts on differential geometry, the author would usually invoke the phrase "locally looks like" when it comes to defining a manifold. For example, the real line is a ...
1
vote
0answers
32 views

What to call a non-edge in a network?

Suppose I have a network with nodes and some edges between the nodes. If node $x$ and node $y$ have an edge, then we say that $(x,y)$ corresponds to the edge between $x$ and $y$. Now suppose that $x$ ...
1
vote
1answer
26 views

Does a number matrix have its invariant factors??

I'm just confused by the following statement in my advanced algebra textbook: Frobenius Form: Let $A$ be an $n$th order square matrix over a number field $K$, whose invariant factors are: ...
2
votes
3answers
74 views

What does it mean if a function is onto? [duplicate]

I've heard the term "onto" several times but still not sure what it means or implies. It's often said along with the function is "one-to-one".
1
vote
0answers
28 views

Union of two graphs with exactly one common vertex

Does this operation (in the title) have a name? According to the Graph Union operation definition vertex sets of two graphs must be disjoint, however I'd like to define an iterative process of graph ...
3
votes
1answer
82 views

Name of the matrix transform $AA^*$ given A?

There are a number of places this matrix transform making its appearance: Every positive semi-definite matrix $B$ can have a decomposition $B=AA^*$ If the matrix $A$ is a lower triangular matrix ...