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Type of matrix in algebraic graph theory
algebraic graph theory, the degree matrix of an undirected graph is a diagonal matrix which contains information about the degree of each vertex—that is,
Degree_matrix
Matrix representation of a graph
theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian, is a matrix representation of a
Laplacian_matrix
Square matrix used to represent a graph or network
degree matrix, which contains information about the degree of each vertex. For a simple graph with vertex set U = {u1, ..., un}, the adjacency matrix
Adjacency_matrix
1999 film by the Wachowskis
The Matrix is a 1999 science fiction action film written and directed by the Wachowskis. The first installment in the Matrix film series, it stars Keanu
The_Matrix
Array of numbers
In mathematics, a matrix (pl.: matrices) is a rectangular array of numbers or other mathematical objects with elements or entries arranged in rows and
Matrix_(mathematics)
On the number of spanning trees in a graph
Laplacian matrix L of G is the difference between the graph's degree matrix (the diagonal matrix of vertex degrees) and its adjacency matrix (a (0,1)-matrix with
Kirchhoff's_theorem
Area of discrete mathematics
adjacency matrix. It also focuses on the Laplacian matrix of a graph, which involves the degree matrix (a diagonal matrix that represents the degree of a vertex)
Graph_theory
matrix that describes adjacency in bipartite graphs. Degree matrix — a diagonal matrix defining the degree of each vertex in a graph. Edmonds matrix —
List_of_named_matrices
Matrix with a multiplicative inverse
algebra, an invertible matrix (non-singular, non-degenerate or regular) is a square matrix that has an inverse. In other words, if a matrix is invertible, it
Invertible_matrix
Matrix of geometric progressions
In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row:
Vandermonde_matrix
Matrix representing a Euclidean rotation
rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix R = [
Rotation_matrix
Degree of connectedness within a graph
connection strengths, as in a stochastic matrix. Katz centrality is a generalization of degree centrality. Degree centrality measures the number of direct
Centrality
Measure of covariance of components of a random vector
covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the
Covariance_matrix
For a square matrix, the transpose of the cofactor matrix
classical adjoint adj(A) of a square matrix A is the transpose of its cofactor matrix. It is occasionally known as adjunct matrix, or "adjoint", though that normally
Adjugate_matrix
Fictional character in The Matrix
the Matrix to an unprecedented degree. She then kisses him, whereupon he miraculously returns to life both in the real world and within the Matrix. The
Trinity_(The_Matrix)
Matrix equal to its conjugate-transpose
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a square matrix with complex-valued entries that is equal to its own conjugate transpose
Hermitian_matrix
1985 American action film by Mark L. Lester
The assassins attack Matrix's secluded mountain home and kidnap his young daughter, Jenny. While trying to intercept them, Matrix is tranquilized and abducted
Commando_(1985_film)
Algorithmic runtime requirements for common math procedures
that either of two different conjectures would imply that the exponent of matrix multiplication is 2. Algorithms for computing transforms of functions (particularly
Computational complexity of mathematical operations
Computational_complexity_of_mathematical_operations
Two-dimensional matrix barcode
A Data Matrix is a two-dimensional code consisting of black and white "cells" or dots arranged in either a square or rectangular pattern, also known as
Data_Matrix
Mathematical concept in algebra
In linear algebra, a nilpotent matrix is a square matrix N such that N k = 0 {\displaystyle N^{k}=0\,} for some positive integer k {\displaystyle k}
Nilpotent_matrix
Concepts from linear algebra
and the degree of this polynomial is n, the order of the matrix A. Its coefficients depend on the entries of A, except that its term of degree n is always
Eigenvalues_and_eigenvectors
Fictional character in The Matrix
Matrix Reloaded, The Matrix Revolutions and The Matrix Resurrections, and one of the protagonists of the video game Enter the Matrix. Niobe also appears
Niobe_(The_Matrix)
Matrix of partial derivatives of a vector-valued function
vector calculus, the Jacobian matrix (/dʒəˈkoʊbiən/, /dʒɪ-, jɪ-/) of a vector-valued function of several variables is the matrix of all its first-order partial
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Special kind of square matrix
In mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal
Triangular_matrix
Advanced academic degree in engineering
from bachelor's to doctoral level according to the degree matrix level. In Latin America, a degree or title of "Ingeniero" is awarded after completing
Engineer's_degree
Matrix of second derivatives
In mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued function
Hessian_matrix
Number of values in the final calculation of a statistic that are free to vary
is important to estimate the Degrees of Freedom permitted by the H {\displaystyle H} matrix so that the residual degrees of freedom can then be used to
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Class of artificial neural networks
the graph adjacency matrix with the addition of self-loops, D ~ {\displaystyle {\tilde {\mathbf {D} }}} is the graph degree matrix with the addition of
Graph_neural_network
Real square matrix whose columns and rows are orthogonal unit vectors
In linear algebra, an orthogonal matrix or orthonormal matrix Q, is a real-valued square matrix whose columns and rows are orthonormal vectors. One way
Orthogonal_matrix
List of values for comparison
(Poor, 0)}. A conventional decision matrix is a special case of belief decision matrix when only one belief degree in a belief structure is 1 and the others
Decision_matrix
Mathematical form
are multiplied, the product usually depends on the order of the factors. Matrix multiplication, for example, is non-commutative, and so is multiplication
Product_(mathematics)
Optical phenomenon
the "degree of polarization"; i.e., the fraction of the total intensity contributed by the completely polarized component. The coherency matrix is not
Unpolarized_light
Matrix of binary truth values
matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain B = {0, 1}. Such a matrix can
Logical_matrix
Sum of elements on the main diagonal
In linear algebra, the trace of a square matrix A, denoted tr(A), is defined as a sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle
Trace_(linear_algebra)
Python library for graphs and networks
matrix of the graph. A Laplacian matrix L of a graph is defined as L = D − A {\displaystyle L=D-A} , where D {\displaystyle D} is the degree matrix (a
NetworkX
Matrix decomposition
(also known as eigenvalue decomposition or EVD) is a factorization of a matrix A {\displaystyle A} into a canonical form given by A = V D V T {\displaystyle
Eigendecomposition of a matrix
Eigendecomposition_of_a_matrix
Arithmetic operation
division can also be defined in terms of the Hadamard product. Because matrix multiplication is not commutative, one can also define a left division or
Division_(mathematics)
Structural support for biological cells
In biology, the extracellular matrix (ECM), also called the intercellular matrix, is a network consisting of extracellular macromolecules and minerals
Extracellular_matrix
Form of a matrix indicating its eigenvalues and their algebraic multiplicities
up an algebraic variety of a low fixed degree in the ambient matrix space. Sets of representatives of matrix conjugacy classes for Jordan normal form
Jordan_normal_form
Graph with oriented edges
i. The adjacency matrix of a directed graph is a logical matrix, and is unique up to permutation of rows and columns. Another matrix representation for
Directed_graph
Polynomial whose roots are the eigenvalues of a matrix
algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots. It
Characteristic_polynomial
Graph where most nodes are reachable in a small number of steps
social connections between any two people (this effect is known as six degrees of separation). Specifically, a small-world network is defined to be a
Small-world_network
Arithmetic operation, inverse of nth power
index or degree, and the number x of which the root is taken is the radicand. A root of degree 2 is called a square root and a root of degree 3, a cube
Nth_root
Computer vision geometry concept
In computer vision a camera matrix or (camera) projection matrix is a 3 × 4 {\displaystyle 3\times 4} matrix which describes the mapping of a pinhole camera
Camera_matrix
Quantum variations of random walks
{\displaystyle D_{G}} and A G {\displaystyle A_{G}} are the degree matrix and the adjacency matrix, respectively. Common choices of graphs that show up in
Quantum_walk
Matrix operation generalizing exponentiation of scalar numbers
In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems
Matrix_exponential
Network that allows computers to share resources and communicate with each other
list / matrix Incidence list / matrix Types Bipartite Complete Directed Hyper Labeled Multi Random Weighted Metrics Algorithms Centrality Degree Motif
Computer_network
Matrix with the same number of rows and columns
mathematics, a square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order n {\displaystyle
Square_matrix
Measure of network community structure
to community 2, s v = − 1 {\displaystyle s_{v}=-1} . Let the adjacency matrix for the network be represented by A {\displaystyle A} , where A v w = 0
Modularity_(networks)
Mathematical function, inverse of an exponential function
the logarithm. For example, the logarithm of a matrix is the (multi-valued) inverse function of the matrix exponential. Another example is the p-adic logarithm
Logarithm
Boston Consulting Group business analysis method
The growth–share matrix (also known as the product portfolio matrix, Boston Box, BCG-matrix, Boston matrix, Boston Consulting Group portfolio analysis
Growth–share_matrix
Concept in linear algebra
In linear algebra, a matrix pencil is a matrix-valued function defined on a field K {\displaystyle K} , usually the real or complex numbers. Let K {\displaystyle
Matrix_pencil
Analog of the continuous Laplace operator
diag(sum(Adj, 2)); % Compute the degree matrix L = Deg - Adj; % Compute the laplacian matrix in terms of the degree and adjacency matrices [V, D] = eig(L);
Discrete_Laplace_operator
Scale-free network generation algorithm
scale-free and certainly contain few nodes (called hubs) with unusually high degree as compared to the other nodes of the network. The BA model tries to explain
Barabási–Albert_model
Approximate nearest neighbor search algorithm
list / matrix Incidence list / matrix Types Bipartite Complete Directed Hyper Labeled Multi Random Weighted Metrics Algorithms Centrality Degree Motif
Hierarchical navigable small world
Hierarchical_navigable_small_world
Projection of data onto lower-dimensional manifolds
to faithfully represent a Markov matrix, K {\displaystyle K} must be normalized by the corresponding degree matrix D {\displaystyle D} : P = D − 1 K
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
Determinant of a subsection of a square matrix
In linear algebra, a minor of a matrix A is the determinant of some smaller square matrix generated from A by removing one or more of its rows and columns
Minor_(linear_algebra)
Standard hostname for a networked device's loopback interface
list / matrix Incidence list / matrix Types Bipartite Complete Directed Hyper Labeled Multi Random Weighted Metrics Algorithms Centrality Degree Motif
Localhost
Cellular automaton
\Delta =D-A} , where D {\displaystyle D} is the degree matrix and A {\displaystyle A} is the adjacency matrix of the graph. Deleting the row and column of
Abelian_sandpile_model
Metaphor for a choice of truth or illusion
reality with the blue pill. The pills were used as props in the 1999 film The Matrix. The trope of a "red pill" as a symbol of a return to reality made its first
Red_pill_and_blue_pill
One of the four basic arithmetic operations
{\text{base}}^{\text{power}}\end{matrix}}\right\}\,=\,} power {\displaystyle \scriptstyle {\text{power}}} nth root (√) radicand degree = {\displaystyle \scriptstyle
Subtraction
Deliberate process that transforms inputs to outputs with variable change
{\text{base}}^{\text{power}}\end{matrix}}\right\}\,=\,} power {\displaystyle \scriptstyle {\text{power}}} nth root (√) radicand degree = {\displaystyle \scriptstyle
Calculation
Study of graphs as a representation of relations between discrete objects
three methods to quantify degree correlations. The recurrence matrix of a recurrence plot can be considered as the adjacency matrix of an undirected and unweighted
Network_theory
Arithmetical operation
associativity, and inclusion of identity (the identity matrix) and inverses. However, matrix multiplication is not commutative, which shows that this
Multiplication
Matrix whose entries are polynomials
whose coefficients are matrices. A univariate polynomial matrix A {\displaystyle A} of degree n {\displaystyle n} is defined as: A ( x ) = ∑ i = 0 n A
Polynomial_matrix
Square matrices satisfy their characteristic equation
case of a matrix of any degree”. The general case was first proved by Ferdinand Frobenius in 1878. For a 1 × 1 {\displaystyle 1\times 1} matrix A = (a)
Cayley–Hamilton_theorem
Clustering and community detection algorithm
partition a graph. The equation for this metric is defined for an adjacency matrix, A, as: Q = 1 2 m ∑ i j ( A i j − k i k j 2 m ) δ ( c i , c j ) {\displaystyle
Leiden_algorithm
Mathematical theory on behavior of connected clusters in a random graph
) {\displaystyle 1/(z-1)} . For a random tree-like network without degree-degree correlation, it can be shown that such network can have a giant component
Percolation_theory
Matrix that commutes with its conjugate transpose
In mathematics, a complex square matrix A is normal if it commutes with its conjugate transpose A*: A normal ⟺ A ∗ A = A A ∗ . {\displaystyle A{\text{
Normal_matrix
Matrices important in quantum mechanics and the study of spin
45 degree polarization (right/left), and circular polarization (right/left). Each Pauli matrix is Hermitian, and together with the identity matrix I {\displaystyle
Pauli_matrices
American actor (born 1986)
drama The Trial of the Chicago 7 (2020), and Morpheus / Agent Smith in The Matrix Resurrections (2021). For his portrayal of Cal Abar / Doctor Manhattan in
Yahya_Abdul-Mateen_II
Mathematical concept in algebra
has the maximal degree), which happens in particular whenever the characteristic polynomial has only simple roots, then the other matrix can be written
Commuting_matrices
Social structure made up of a set of social actors
sociology and social movements, and Stanley Milgram, who developed the "six degrees of separation" thesis. Mark Granovetter and Barry Wellman are among the
Social_network
Notion in statistics
some initial results by Francis Ysidro Edgeworth). The Fisher information matrix is used to calculate the covariance matrices associated with maximum-likelihood
Fisher_information
Used for the resultant of two polynomials
matrix is a matrix associated to two univariate polynomials with coefficients in a field or a commutative ring. The entries of the Sylvester matrix of
Sylvester_matrix
Matrix decomposition
complex matrix into a rotation, followed by a scaling, followed by another rotation. It generalizes the eigendecomposition of a square normal matrix with
Singular_value_decomposition
Matrix that, squared, equals itself
linear algebra, an idempotent matrix is a matrix which, when multiplied by itself, yields itself. That is, the matrix A {\displaystyle A} is idempotent
Idempotent_matrix
2003 American-Japanese-South Korean anthology anime film
includes nine animated short films, some of which provide backstory for The Matrix film series, while others present side stories. The Animatrix was released
The_Animatrix
Matrix whose determinant is a resultant
In mathematics, a Bézout matrix (or Bézoutian or Bezoutiant) is a special square matrix associated with two polynomials, introduced by James Joseph Sylvester
Bézout_matrix
Method of generating random small-world graphs
coefficient. They do not account for the formation of hubs. Formally, the degree distribution of ER graphs converges to a Poisson distribution, rather than
Watts–Strogatz_model
Mathematical result of division
{\text{base}}^{\text{power}}\end{matrix}}\right\}\,=\,} power {\displaystyle \scriptstyle {\text{power}}} nth root (√) radicand degree = {\displaystyle \scriptstyle
Quotient
Square matrix constructed from a monic polynomial
In linear algebra, the Frobenius companion matrix of the monic polynomial p ( x ) = c 0 + c 1 x + ⋯ + c n − 1 x n − 1 + x n {\displaystyle p(x)=c_{0}+c_{1}x+\cdots
Companion_matrix
Network whose degree distribution follows a power law
A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction P(k) of nodes in the network
Scale-free_network
Algebraic object with geometric applications
components form an array, which can be thought of as a high-dimensional matrix. Tensors have become important in physics, because they provide a concise
Tensor
Skew-symmetric 4 × 4 matrix, which characterizes a straight line in projective space
mathematics, the Plücker matrix is a special skew-symmetric 4 × 4 matrix, which characterizes a straight line in projective space. The matrix is defined by 6 Plücker
Plücker_matrix
Square root of the determinant of a skew-symmetric square matrix
determinant of an m-by-m skew-symmetric matrix can always be written as the square of a polynomial in the matrix entries, a polynomial with integer coefficients
Pfaffian
Matrix decomposition
factorization, is a decomposition of a matrix A into a product A = QR of an orthonormal matrix Q and an upper triangular matrix R. QR decomposition is often used
QR_decomposition
Model of neutrino oscillation
matrix (PMNS matrix), Maki–Nakagawa–Sakata matrix (MNS matrix), lepton mixing matrix, or neutrino mixing matrix is a unitary mixing matrix that contains
Pontecorvo–Maki–Nakagawa–Sakata matrix
Pontecorvo–Maki–Nakagawa–Sakata_matrix
Generalization of gamma distribution to multiple dimensions
positive integer n is the number of degrees of freedom. Sometimes this is written W(V, p, n). For n ≥ p the matrix S is invertible with probability 1 if
Wishart_distribution
Square matrix containing the distances between elements in a set
mathematics, computer science and especially graph theory, a distance matrix is a square matrix (two-dimensional array) containing the distances, taken pairwise
Distance_matrix
Filling in missing entries of a matrix
indicated document. Without any restrictions on the number of degrees of freedom in the completed matrix, this problem is underdetermined since the hidden entries
Matrix_completion
Data structure representing a graph
proportional to the logarithm of the degree. The main alternative to the adjacency list is the adjacency matrix, a matrix whose rows and columns are indexed
Adjacency_list
https://projects.kora.matrix.msu.edu/files/162-565-1308/S201_2010S.pdf Commencement 2010 Spring Semester: Candidates-Spring and Summer, 2010 – Degree of Doctor of
List of artists and entertainers with advanced degrees
List_of_artists_and_entertainers_with_advanced_degrees
Polynomial with a matrix as variable
In mathematics, a matrix polynomial is a polynomial with square matrices as variables. Given an ordinary, scalar-valued polynomial P ( x ) = ∑ i = 0 n
Matrix_polynomial
Academic field
alternate approach to network probability structures is the network probability matrix, which models the probability of edges occurring in a network, based on
Network_science
Concept in statistics
statistics, the projection matrix ( P ) {\displaystyle (\mathbf {P} )} , sometimes also called the influence matrix or hat matrix ( H ) {\displaystyle (\mathbf
Projection_matrix
Concept in network science
of graphs and networks, the degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability
Degree_distribution
Concept in topology
{\displaystyle Df(y)} is the Jacobian matrix of f {\displaystyle f} in y {\displaystyle y} . This definition of the degree may be naturally extended for non-regular
Degree of a continuous mapping
Degree_of_a_continuous_mapping
Material made from a combination of two or more unlike substances
resin or thermoplastics as a binder Ceramic matrix composites (composite ceramic and metal matrices) Metal matrix composites Advanced composite materials
Composite_material
Matrix-valued random variable
probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled
Random_matrix
DEGREE MATRIX
DEGREE MATRIX
Boy/Male
Arabic, Indian
Decree; Edict
Male
English
Variant spelling of English Daren, DERREN means "from Araines."
Girl/Female
Australian, French
The One Desired; Similar to Desiree; Desired; Longed for
Female
English
English variant spelling of French Désirée, DEZIREE means "desired."
Boy/Male
Arabic
Degrees; Dignities
Girl/Female
Muslim
Increase, Excess, High degree
Girl/Female
Gujarati, Hindu, Indian, Malayalam
A Decree; Command
Boy/Male
Muslim
Order, Decree
Girl/Female
Hindu
A decree, Command
Girl/Female
Tamil
A decree, Command
Girl/Female
Hindu, Indian
A Decree; Command
Girl/Female
Muslim
The utmost, Highest degree
Boy/Male
Muslim
Decree. Edict.
Girl/Female
Arabic, Australian, Muslim
The Utmost; Highest Degree
Girl/Female
Indian
Utmost point, Degree
Girl/Female
Muslim
Utmost point, Degree
Girl/Female
Indian
Increase, Excess, High degree
Boy/Male
Arabic
Degrees; Dignities
Male
English
English name derived from Dutch Diederik, DEREK means "first of the people; king of nations."
Boy/Male
Indian
Order, Decree
DEGREE MATRIX
DEGREE MATRIX
Boy/Male
African
My turn.
Boy/Male
Muslim
Guidance, Rectitude
Boy/Male
Indian
Who Seeks Less
Female
Croatian
, the light (?), or, fir tree (?).
Boy/Male
English
From the south cliff.
Girl/Female
Tamil
Name of a star
Girl/Female
Hindu, Indian, Tamil
Goddess Earth; Wife of Sage Kashyap; Sweetest; Noisy; High Pitched; Swift Flowing; A Star
Girl/Female
Tamil
Achievement, Perfection, Success
Boy/Male
Gujarati, Hindu, Indian, Kannada, Traditional
Lord Shiva's Son
Girl/Female
Muslim
True believer, Pure Muslim
DEGREE MATRIX
DEGREE MATRIX
DEGREE MATRIX
DEGREE MATRIX
DEGREE MATRIX
n.
Measure of advancement; quality; extent; as, tastes differ in kind as well as in degree.
n.
Three figures taken together in numeration; thus, 140 is one degree, 222,140 two degrees.
v. i.
To agree.
v. t.
To reduce from a higher to a lower rank or degree; to lower in rank; to deprive of office or dignity; to strip of honors; as, to degrade a nobleman, or a general officer.
n.
Grade or rank to which scholars are admitted by a college or university, in recognition of their attainments; as, the degree of bachelor of arts, master, doctor, etc.
imp. & p. p.
of Decree
n.
A decree.
n.
A certain distance or remove in the line of descent, determining the proximity of blood; one remove in the chain of relationship; as, a relation in the third or fourth degree.
v. t.
To admit, or come to one mind concerning; to settle; to arrange; as, to agree the fact; to agree differences.
v. t.
To determine judicially by authority, or by decree; to constitute by edict; to appoint by decree or law; to determine; to order; to ordain; as, a court decrees a restoration of property.
v. i.
To agree again.
n.
One of a series of progressive steps upward or downward, in quality, rank, acquirement, and the like; a stage in progression; grade; gradation; as, degrees of vice and virtue; to advance by slow degrees; degree of comparison.
a.
Dearer.
v. i.
To make decrees; -- used absolutely.
n.
State as indicated by sum of exponents; more particularly, the degree of a term is indicated by the sum of the exponents of its literal factors; thus, a2b3c is a term of the sixth degree. The degree of a power, or radical, is denoted by its index, that of an equation by the greatest sum of the exponents of the unknown quantities in any term; thus, ax4 + bx2 = c, and mx2y2 + nyx = p, are both equations of the fourth degree.
v. t.
To experience regret on account of; to lose or miss with a sense of regret; to feel sorrow or dissatisfaction on account of (the happening or the loss of something); as, to regret an error; to regret lost opportunities or friends.
n.
A 360th part of the circumference of a circle, which part is taken as the principal unit of measure for arcs and angles. The degree is divided into 60 minutes and the minute into 60 seconds.
n.
Rank; degree; position.
n.
One who decrees.
n.
An edict or law made by a council for regulating any business within their jurisdiction; as, the decrees of ecclesiastical councils.