Tagged Questions
3
votes
1answer
31 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
33 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
...
0
votes
0answers
34 views
Name of the inverse of a reduced node-arc incidence matrix
So I basically have a directed incidence matrix 'A' and its inverse 's' has been labelled as "sensitivity matrix"; is that right? {the label is a comment in a matlab program}
Also, it's been said ...
1
vote
0answers
46 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?
2
votes
0answers
47 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 e_1) ...
2
votes
2answers
113 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
45 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
66 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.
...
1
vote
2answers
137 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
99 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
29 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
167 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
58 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
68 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$$
with $P$ an $n\times n$ and $Q$ an $m\times m $ matrix.
Is there a standard terminolgy for this relation? If instead of ...
2
votes
2answers
507 views
Relation between Interior Product, Inner Product, Exterior Product, Outer Product..
Following my previous question Relation between cross-product and outer product where I learnt that the Exterior Product generalises the Cross Product whereas the Inner Product generalises the Dot ...
2
votes
1answer
634 views
Relation between cross-product and outer product
If inner products ($V$) are generalisations of dot products ($ \mathbb{R}^n$), then are outer products ($V$) also related to cross-products ($ \mathbb{R}^3$) in some way?
A quick search reveals that ...
3
votes
2answers
209 views
Does “nullity” have a potentially conflicting or confusing usage?
In Linear Algebra and Its Applications, David Lay writes, "the dimension of the null space is sometimes called the nullity of A, though we will not use the term." He then goes on to specify "The Rank ...
3
votes
2answers
135 views
Does this kind of matrix have a name?
Are these kind of matrices generally known in mathematics?
Do they have a name?
$$
\left[\begin{array}{rrr}
A & B \\
B & A \\
\end{array}\right]
$$
$$
\left[\begin{array}{rrr}
...
2
votes
1answer
64 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
80 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
133 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
106 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?
0
votes
1answer
146 views
What is generic rank?
What is meant by generic rank of a matrix? Is it something different from the rank, and does the word generic has just its English meaning?
I came across this term in the book "Algebraic statistics ...
0
votes
0answers
57 views
Is there a term for the “opposite” location in a matrix?
I'm just looking for the correct term to describe a concept:
Suppose I have a 5x5 matrix:
A B C D E
F G H I J
K L M N O
P Q R S T
U V W X Y
I can pick any two cells, let's say the cells I and Q, ...
0
votes
1answer
80 views
Positive semidefinite vector $\bar{x}$ as $\bar{x}>0 :=\bar{x} \lambda \bar{x}^{T}>0$?
$A \lambda A^{T} $ (quadratic form?) is used with matrices to check definiteness. What about with vectors? If I see conditions such as $\bar{x} > 0$, how can I know whether it means $\bar{x}_{i} ...
1
vote
1answer
158 views
Is there any math operation defined to obtain vector $[4,3,2,1]$ from $[1,2,3,4]$?
I mean have it been studied, does it have a name?
Like Transpose, Inverse, etc.. have names.
I wonder if the "inversion" of the components position have a name so then I could search material on ...
1
vote
1answer
62 views
Dimension and size of an array, matrix, vector
For a $1 \times n$ or $n \times 1$ vector, I remember people say it
is n-dimensional.
For a $n \times m$ matrix, I heard it is said to have size $n \times
m$. As to its dimension, quoted from ...
1
vote
0answers
36 views
Is there a particular name for a'long-small-small' tensor/array?
I'm thinking of a 3D array, with dimensions small,small,large.
I've taken to saying 'sausage' as shorthand (and I'm sure there are worse NSFW descriptions) but is there a 'legitimate' description for ...
1
vote
3answers
138 views
Matrix with exactly one 1 in each row
Is there a name associated to rectangular matrices $M \times N$ that have exactly one entry equal to $1$ in each row and $0$ everywhere else?
2
votes
1answer
225 views
Do these matrices have a name?
I'm wondering if these matrices have a name? (I'm somehow tempted to call them subunitary but it seems to be reserved for something else.)
The matrix $M \in \mathbb{C}^{n\times n}$ is called ..., if ...
1
vote
2answers
139 views
What is the name for a function of a matrix that changes the matrix size?
I have a set of functions that map square matrices with $n$ rows and columns to square matrices with $k < n$ rows and columns. Is there a name for this property? I know that 'projection' would be ...
