2
votes
0answers
44 views

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 ...
4
votes
1answer
58 views

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 $Z_{ij} = z_{i}z_{j}$
2
votes
1answer
33 views

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 ...
1
vote
1answer
33 views

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?
1
vote
0answers
25 views

term for a sum of diagonal and skew-symmetric matrix?

Is there a term for a matrix that is a sum of a diagonal and a skew-symmetric matrix? One particular example of this is a 2x2 matrix of the form $$ M = \begin{bmatrix} a & b \\ -b & a ...
0
votes
0answers
58 views

What is the operation inverse to vectorization (vec operator)?

There is a well knows vectorization operation in matrix analysis $\mbox{vec}$: https://en.wikipedia.org/wiki/Vectorization_%28mathematics%29 I've vectorized my matrix equations, did some ...
0
votes
0answers
17 views

Maximal angle between kernel of rows of a matrix

Consider a matrix with 2 columns $$ \begin{pmatrix} a_1 & b_1 \\ a_2 & b_2 \\ a_3 & b_3 \\ \vdots & \vdots \end{pmatrix} . $$ To each row $(a_i \;\;\; b_i)$, one draws the kernel ...
3
votes
1answer
46 views

Is there a way in matrix math notation to show the 'flip up-down', and 'flip left-right' of a matrix?

Title says it all - is there an accepted mathematical way in matrix notation to show those operations on a matrix? Thanks.
0
votes
1answer
31 views

Is there a general name for matrices which only have zeros on their main diagonal?

A diagonal matrix is one where every component not on the main diagonal is zero. E.g. $$ \begin{array}{cc} 12 & 0 & 0\\ 0 & 0 & 0\\ 0 & 0 & -2 \end{array} $$ Is there a term ...
0
votes
2answers
42 views

About matrix $R$, what is this called: $R^TR$? What is it for?

I am doing singular value decomposition on a matrix $R$. The first step is to compute such a matrix $R^TR$. What is this matrix? A reference told me this is cross product of matrix R. I use a ...
1
vote
1answer
43 views

Matrices and what they represent

I know matrices can represent transformations but they can also represent the points that are transformed by another matrix do these two types have different names and if so what are they?? thanks
1
vote
0answers
77 views

Whats the name of this sort of matrix

What the name of such a matrix \begin{pmatrix} 1 & 2 & 5 & 10 \\ 3 & 4 & 7 & 12 \\ 6 & 8 & 9 & 14 \\ 11 & 13 & 15 & 16\\ \end{pmatrix} Its properties ...
1
vote
1answer
45 views

Name for multiples of orthogonal matrices

Is there a name for a matrix which is a multiple of an orthogonal matrix? I.e. a square matrix $A$ which satisfies the condition $$A^TA = AA^T = \lambda I$$ where $\lambda$ is some scalar (which ...
0
votes
2answers
29 views

Line in vector form?

Given the line y=3x my book states it is $\left(\begin{array}{c}1 \\ 3\\\end{array}\right)$ as a matrix. Why is it not $\left(\begin{array}{c}3 \\ 1\\\end{array}\right)$, I thought the upper number ...
12
votes
3answers
466 views

Why is an orthogonal matrix called orthogonal?

I know a square matrix is called orthogonal if its rows (and columns) are pairwise orthonormal But is there a deeper reason for this, or is it only an historical reason? I find it is very confusing ...
1
vote
1answer
74 views

What is matrix inequality such as $A>0$ or $A\succ 0$?

I am trying to gather here different meanings of the same symbol, inequality symbol or the succ symbol. I find many other use them so many different ways. Sometimes, $A>0$ means $\bar x^T A \bar x ...
1
vote
2answers
47 views

Matrix with Functions as Entries

What do we call a matrix with functions as entries? $$\textbf{f(x)}=\begin{bmatrix} f_{11}(x) & f_{12}(x) \\ f_{21}(x) & f_{22}(x) \end{bmatrix} $$
2
votes
1answer
56 views

Adjoint of a Matrix Definition

Tom M. Apostol in his book "calculus Vol. 2" page 122 (see image below) defines adjoint of a matrix as the transpose of the conjugate of the matrix. Is this definition always correct ? Does it agree ...
1
vote
1answer
79 views

Some basic questions about matrix rings and reversibility.

Neither commutative rings nor division rings are viable approaches to studying rings of matrices. However, there is a very cool notion of a reversible ring, which looks like it can fill this void. I ...
1
vote
0answers
36 views

Is there a special name for matrices with $M[j,i] = M[i,i] - k, i \neq j$?

Backgroud: I am working on a computer science problem and arrives at a matrix $M$ with the following property: The size of Matrix $M$ is $n\times n$. For each row $j$, we have $M[j,i] = ...
25
votes
2answers
1k views

Word origin / meaning of 'kernel' in linear algebra

It may be the dumbest question ever asked on math.SE, but... Given a real matrix $\mathbf A\in\mathbb R^{m\times n}$, the column space is defined as $$C(\mathbf A) = \{\mathbf A \mathbf x : ...
0
votes
0answers
22 views

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 ...
0
votes
2answers
34 views

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 ...
1
vote
1answer
53 views

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 ...
1
vote
0answers
51 views

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: ...
1
vote
0answers
56 views

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 $X=\{1,1,2,3,3\}$ ...
1
vote
1answer
32 views

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 ...
0
votes
2answers
69 views

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.
1
vote
1answer
28 views

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?
3
votes
1answer
45 views

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 ...
0
votes
0answers
107 views

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 ...
4
votes
1answer
184 views

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?
3
votes
0answers
118 views

matrix representation of operator

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 ...
2
votes
2answers
269 views

What are matrix coefficients in linear algebra?

What are matrix coefficients in linear algebra? And what does it mean "integer matrix coefficients"?
0
votes
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. ...
0
votes
1answer
160 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. ...
3
votes
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 ...
1
vote
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 ...
0
votes
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 ...
2
votes
1answer
487 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?
0
votes
1answer
129 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?
5
votes
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 ...
3
votes
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 ...
5
votes
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 ...
3
votes
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 ...
3
votes
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} ...
2
votes
1answer
74 views

Is there a special name for matrices consist of repeated unit vectors?

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 ...
1
vote
1answer
162 views

Generalization of the matrix concept

It has been some time since I left university... In a not too formal language, an $n$-dimensional vector is an indexed set of numbers $\{i_1, ..., i_n\}$. A $n\times m$ matrix is a set of numbers ...
1
vote
1answer
164 views

Semigroups of matrices with zeroes and a single 1

I stumbled upon this while reviewing a Harvard lecture on abstract algebra. What I want to know is if these semigroups are known and, if so, what they are called. I've checked the assertions below for ...
3
votes
1answer
145 views

Matrices of Trace $0$

The set of all $n$-square matrices with trace $0$ is a subspace of the set of all $n$-square matrices. Is there a standard notation and/or name for this subspace?