# Tagged Questions

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### What do you call a matrix where the rows sum to zero and the columns sum to zero?

What do you call a matrix where the rows sum to zero and the columns sum to zero? Or is there no standard name for this type of matrix?
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### Is a set of some $m \times n$ matrices a relation?

A relation between sets $A_i, i = 1, \dots, n$ is defined as a subset of $\prod_i A_i$. Given $m, n \in \mathbb N$, is a set of (some or all) $m \times n$ matrices over $\mathbb R$ considered a ...
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### Is there a name for the following type of block matrices?

Is there a name for the following type of block matrices? A matrix $A$ is [insert name here] if it can be decomposed into non-zero non-scalar submatrices such that each sub-matrix $B$, with $B$ ...
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### What do you call the following operations on a symmetric matrix?

Suppose we have a symmetric matrix of the following form, where the diagonal is always zero: \begin{array}{cccc} 0 & 1 & 1 & 0\\ 1 & 0 & 1 & 1\\ 1 & 1 & 0 & 0\\ 0 ...
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### What is the name of the matrix that is created by a vector times its transpose.

I am looking for the name of the matrix created by the following operation: $Z = z*z^T$ I know it should create a symmetric matrix with an element $Z_{ij} = z_{i}z_{j}$
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### Matrices with the same characteristic polynomial

For all the $n \times n$ matrices, let's define an equivalent relation that two matrices are in the relation iff they have the same characteristic polynomial. How can we characterize the matrices ...
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### Any name for a special matrix with only non-zero entry

Consider an $n\times n$ matrix $\mathbf{E}_{ij}$ which is 1 at entry $(i,j)$ and zero everywhere else. Is there any special name for this kind of matrices?
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### What's the name for a matrix with a mostly dominant diagonal band

What's the name of a matrix with higher values / more non-zero values close to the diagonal? The non-zero entries are not restricted to a band around the diagonal. In my case, the diagonal itself is ...
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### What is the term to make one matrix from two or more?

I am looking for the proper term for the operation of creating one block matrix from two or more for example $[AB]$ from $A$, $B$. And what is the correct notation to denote such a matrix. Do we use a ...
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### Rowwise matrix multiplication, what is the name of this?

Let $A=\begin{pmatrix} 1 & 2 & 3 \\ 1 & 1 & 1 \end{pmatrix}$ and $\operatorname{SomeOperation}(A)=\begin{pmatrix}1*2*3 \\ 1*1*1\end{pmatrix} =\begin{pmatrix}6 \\ 1\end{pmatrix}$. What ...
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### With infinite size, we can have $P \cdot M = M \cdot D$ (D diagonal) but where $M^{-1}$ does not exist. Can we say “P is diagonalizable”?

(I had this question in mind for longer time, but it is just triggered now by some comments at that recent question in mse) (Background) I was looking at properties of the Pascal-matrix: ...
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### Terminology for matrix whose rows are permutations of a given multiset.

Let $X=\{a_{1},a_{2},\ldots,a_{m}\}$ be a multiset. Is there a name for an $n\times m$ matrix $A$ such that the entries of each row of $A$ are equal to the set $X$. For example, if $X=\{1,1,2,3,3\}$ ...
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### Is there a proper term to refer to something that can either be a row or a column of a matrix?

Let $A$ be a $m \times n$ matrix; if I label the rows as numbers, so that the sets of rows is $$R=\{0,\dots,m-1\}$$ and the set of the columns is $$C=\{m,\dots,m+n-1\}$$ and consider simply the ...
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### Is there a special term for an array consisting only of ones?

Is there a special term for an array consisting only of ones? Sorry for the rather elementary question. I am getting into MapReduce programming and am trying to frame my code to be nice and neat.
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### How to name a matrix with restricted input values?

How should I refer to a matrix with a restricted domain of possible values that can be stored inside?
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### Correct term for “minor matrix”

If I get it right, the minor $M_{i,j}$ for an element $a_{i,j}$ of a matrix A is the determinant of the matrix created from $A$ by excluding the $i^{th}$ row and $j^{th}$ column. But what is a proper ...
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### What is the name for a non-square permutation matrix?

Consider a matrix that selects and permutes some but not all of the entries of a vector. That is a binary $n\times m$ matrix, where $n<m$, with a single one per row, for example ...
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### What is the last index of a third-order tensor called?

In a third-order tensor I guess the first and second index would be called row and column respectively but is there a name for the third index?
Vector $\vec v\$ in basis E = $[\vec e_1 \vec e_2 \ldots \vec e_n]$ $$\vec v = E \ \begin{bmatrix}v_1 \\ v_2 \\ \vdots \\ v_n \end{bmatrix}$$ Now, operator acts upon it $$A(\vec v) = v_1 A(\vec ... 2answers 272 views ### What are matrix coefficients in linear algebra? What are matrix coefficients in linear algebra? And what does it mean "integer matrix coefficients"? 0answers 59 views ### Abbreviations in Combinatorial Graph/Matrix theory I'm getting started with research in combinatorics. I have come across a reference that uses a great deal of abbreviations. I was able to figure most of them out but there are a few that I can find. ... 1answer 168 views ### What is a Jordan Cell? Google has been surprisingly unhelpful for me. A homework problem from my algebra class asks me to Calculate p(A) where A is a Jordan cell and p is a polynomial. ... 2answers 1k views ### Name for diagonals of a matrix I am looking for the terms to use for particular types of diagonals in two dimensional matrices. I have heard the longest diagonal, from top-left element and in the direction down-right often called ... 1answer 100 views ### Name of a particular matrix close to projection I am wondering if there is a special name for an m\times n matrix A=(a_{i,j}), with a_{i,j}\in\{0,1\} that will pick m unique components from a vector v\in\mathbb{R}^n (m\le n), it is ... 1answer 49 views ### Names for special submatrices? Let (a_{ij}), i,j \in \{1,...,n\} be a matrix. What are the names for the following special square submatrices: for any set of indices J⊂{1,2,..,n}, the submatrix (a_{jk})j,k\in J, a ... 1answer 505 views ### Correct name for multi-dimensional array/matrix/tensor What is the correct name for an n-dimensional array in mathematics? I have seen the following: nD-Matrix nD-Array nD-Tensor Which is the right way? 1answer 132 views ### In 3D: column major, row major, … major? If we use column and row major to describe dimension-majority for x and y respectively, what word is commonly used (if any) to describe such majority for the z dimension? 1answer 77 views ### Standard terminology for the relation between A and B if B= Q^t A P? Let A,B be two rectangular m\times n matrices related by$$B= Q^t A P$$with P an n\times n and Q an m\times m  matrix. Is there a standard terminolgy for this relation? If instead of ... 2answers 1k views ### Relation between Interior Product, Inner Product, Exterior Product, Outer Product.. Following my previous question Relation between cross-product and outer product where I learnt that the Exterior Product generalises the Cross Product whereas the Inner Product generalises the Dot ... 1answer 2k views ### Relation between cross-product and outer product If inner products (V) are generalisations of dot products ( \mathbb{R}^n), then are outer products (V) also related to cross-products ( \mathbb{R}^3) in some way? A quick search reveals that ... 2answers 229 views ### Does “nullity” have a potentially conflicting or confusing usage? In Linear Algebra and Its Applications, David Lay writes, "the dimension of the null space is sometimes called the nullity of A, though we will not use the term." He then goes on to specify "The Rank ... 2answers 146 views ### Does this kind of matrix have a name? Are these kind of matrices generally known in mathematics? Do they have a name?$$ \left[\begin{array}{rrr} A & B \\ B & A \\ \end{array}\right]  \left[\begin{array}{rrr} ...
For example this one: Q=\begin{pmatrix} 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 ...