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Topics referred to by the same term
Matrix element may refer to: The (scalar) entries of a matrix. Matrix element (physics), the value of a linear operator (especially a modified Hamiltonian)
Matrix_element
Linear operator used in quantum mechanics
theory, the matrix element refers to the linear operator of a modified Hamiltonian using Dirac notation. It is in fact referring to the matrix elements of
Matrix_element_(physics)
Square matrix used to represent a graph or network
set U = {u1, ..., un}, the adjacency matrix is a square n × n matrix A such that its element Aij is 1 when there is an edge from vertex ui to vertex uj,
Adjacency_matrix
Networking protocol for real-time communication
which was later renamed to Element matrix services) to generate income. In the early weeks after its creation, the Matrix team and the company Purism
Matrix_(protocol)
Formulation of quantum mechanics
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually
Matrix_mechanics
Decentralised chat and collaboration software
Element (formerly Riot and Vector) is a free and open-source software instant messaging client implementing the Matrix protocol. Element was originally
Element_(software)
Matrix used in finite element analysis
In the finite element method for the numerical solution of elliptic partial differential equations, the stiffness matrix is a matrix that represents the
Stiffness_matrix
Theorem used in quantum mechanics for angular momentum calculations
that does not depend on m, m′, nor q and is referred to as the reduced matrix element. The Wigner–Eckart theorem states indeed that operating with a spherical
Wigner–Eckart_theorem
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
Norm on a vector space of matrices
such norms are referred to as matrix norms. Matrix norms behave in certain ways like the distance from the zero matrix. They are distinguished from the
Matrix_norm
Non-zero element of a matrix selected by an algorithm
The pivot or pivot element is the element of a matrix, or an array, which is selected first by an algorithm (e.g. Gaussian elimination, simplex algorithm
Pivot_element
Matrix in which most of the elements are zero
two-dimensional array. Each entry in the array represents an element ai,j of the matrix and is accessed by the two indices i and j. Conventionally, i
Sparse_matrix
Matrix whose only nonzero elements are on its main diagonal
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices
Diagonal_matrix
Electron-positron scattering
the scattering and annihilation diagrams contribute to the transition matrix element. By letting k and k' represent the four-momentum of the positron, while
Bhabha_scattering
Matrix used in image processing to alter an image
In image processing, a kernel, convolution matrix, or mask is a small matrix used for blurring, sharpening, embossing, edge detection, and more. This
Kernel_(image_processing)
Mathematical operation on invertible matrices
theory since when a matrix has a logarithm then it is in an element of a Lie group and the logarithm is the corresponding element of the vector space
Logarithm_of_a_matrix
Complex matrix A* obtained from a matrix A by transposing it and conjugating each entry
{\displaystyle ij} denotes the ( i , j ) {\displaystyle (i,j)} -th entry (matrix element), for 1 ≤ i ≤ n {\displaystyle 1\leq i\leq n} and 1 ≤ j ≤ m {\displaystyle
Conjugate_transpose
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)
Matrix operation generalizing exponentiation of scalar numbers
t = 1. When X is an n × n diagonal matrix then exp(X) will be an n × n diagonal matrix with each diagonal element equal to the ordinary exponential applied
Matrix_exponential
Random matrix with gaussian entries
2, and 4 respectively, counting the number of real components per matrix element (1 for real elements, 2 for complex elements, 4 for quaternions). The
Gaussian_ensemble
Transition rate formula
initial and final states of the system (described by the square of the matrix element of the perturbation) as well as the density of states. It is also applicable
Fermi's_golden_rule
Decision tracking and managing method
structure matrix (DSM; also referred to as dependency structure matrix, dependency structure method, dependency source matrix, problem solving matrix, incidence
Design_structure_matrix
Pictorial representation of the behavior of subatomic particles
particles or fields. The transition amplitude is then given as the matrix element of the S-matrix between the initial and final states of the quantum system.
Feynman_diagram
Imaging Instrument
the barrier and into the volume of the tip (z > z0). If the tunneling matrix element is defined as M μ ν = ∫ z > z 0 ψ μ S U T ψ ν T ∗ d x d y d z , {\displaystyle
Scanning_tunneling_microscope
Assumption that motions of nuclei and electrons can be separated
whole matrix of P α A {\displaystyle P_{\alpha }^{A}} is effectively zero. The third term on the right side of the expression for the matrix element of Tn
Born–Oppenheimer approximation
Born–Oppenheimer_approximation
Matrix equal to its conjugate-transpose
matrix (or self-adjoint matrix) is a square matrix with complex-valued entries that is equal to its own conjugate transpose. That is, if the element in
Hermitian_matrix
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
Matrix that shows the relationship between two classes of objects
relation. If the first class is X and the second is Y, the matrix has one row for each element of X and one column for each mapping from X to Y. The entry
Incidence_matrix
Specialized notation for multivariable calculus
function with respect to a matrix, known as the gradient matrix, which collects the derivative with respect to each matrix element in the corresponding position
Matrix_calculus
Generalization of additive and multiplicative inverses
identity element, and if e and f are different identities, then e ∗ f {\displaystyle e*f} is not defined. For example, in the case of matrix multiplication
Inverse_element
Matrix representing the effect of scattering on a physical system
In physics, the S-matrix or scattering matrix is a matrix that relates the initial state and the final state of a physical system undergoing a scattering
S-matrix
Numerical method for solving physical or engineering problems
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical
Finite_element_method
Form of a matrix
diagonal elements of a skew-symmetric matrix are zeros because each element must be its own negative. The matrix A = [ 0 2 − 45 − 2 0 − 4 45 4 0 ] {\displaystyle
Skew-symmetric_matrix
Topics referred to by the same term
mathematical treatise on geometry and number theory An entry, or element, of a matrix Classical elements, ancient beliefs about the fundamental types of
Element
Special point in the density of states of a crystal
electronic band structure using Fermi's Golden Rule where the relevant matrix element to be evaluated is the dipole operator A → ⋅ p → {\displaystyle {\vec
Van_Hove_singularity
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
Connection between correlation functions and the S-matrix
describe the system of particles in its entire evolution, so that the S-matrix element: S f i = ⟨ { q } o u t | { p } i n ⟩ {\displaystyle S_{\rm {fi}}=\langle
LSZ_reduction_formula
Concentration of chemical orbitals on adjacent atoms
overlap matrix is always n×n, where n is the number of basis functions used. It is a kind of Gramian matrix. In general, each overlap matrix element is defined
Orbital_overlap
Mathematical operation in linear algebra
columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number
Matrix_multiplication
Matrix operation which flips a matrix over its diagonal
that flips a matrix over its diagonal; that is, transposition switches the row and column indices of the matrix A to produce another matrix, called the
Transpose
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
Algebraic term
unipotent element r of a ring R is one such that r − 1 is a nilpotent element; in other words, (r − 1)n is zero for some n. In particular, a square matrix M is
Unipotent
Algorithm to multiply matrices
Because matrix multiplication is such a central operation in many numerical algorithms, much work has been invested in making matrix multiplication algorithms
Matrix multiplication algorithm
Matrix_multiplication_algorithm
Quantum mechanics principle
|y\rangle {\Big )}} is necessarily antisymmetric. To prove it, consider the matrix element ⟨ ψ | ( ( | x ⟩ + | y ⟩ ) ⊗ ( | x ⟩ + | y ⟩ ) ) . {\displaystyle \langle
Pauli_exclusion_principle
Expectation value of time-ordered quantum operators
calculating scattering amplitudes is the matrix element M {\displaystyle {\mathcal {M}}} which is defined from the S-matrix via ⟨ f | S − 1 | i ⟩ = i ( 2 π )
Correlation function (quantum field theory)
Correlation_function_(quantum_field_theory)
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
Kind of square matrix in linear algebra
algebra, a Hessenberg matrix is a special kind of square matrix, one that is "almost" triangular. To be exact, an upper Hessenberg matrix has zero entries
Hessenberg_matrix
Type of matrix in probability theory and statistics
cross-covariance matrix is a matrix whose element in the i, j position is the covariance between the i-th element of a random vector and j-th element of another
Cross-covariance_matrix
Physical phenomenon
violation by modifying the matrix element to include vector and axial-vector couplings of fermions. This formed the matrix element that completed the Fermi
Beta_decay_transition
Functions on special groups related to their matrix representations
In mathematics, a matrix coefficient (or matrix element) is a function on a group of a special form, which depends on a linear representation of the group
Matrix_coefficient
Type of connective tissue in animals
fibrous tissue, is a type of connective tissue with fibers as its main matrix element. The fibers are mainly composed of type I collagen. Crowded between
Dense_connective_tissue
square of the matrix element. The result of the coherence changes the matrix element M s {\displaystyle M_{s}} into the matrix element M {\displaystyle
Mattis–Bardeen_theory
Elementwise product of two matrices
a matrix of the multiplied corresponding elements. This operation can be thought as a "naive matrix multiplication" and is different from the matrix product
Hadamard_product_(matrices)
Vector operation
two coordinate vectors is the matrix whose entries are all products of an element in the first vector with an element in the second vector. If the two
Outer_product
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
System for describing optical polarization
particular optical element is represented by a Mueller matrix—a 4×4 matrix that is an overlapping generalization of the Jones matrix. Disregarding coherent
Mueller_calculus
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)
Matrix defined using smaller matrices called blocks
In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices
Block_matrix
Lossy compression technique
scale code and divided element-wise by the quantization matrix, and rounding each resultant element. The quantization matrix is designed to provide more
Quantization (image processing)
Quantization_(image_processing)
Most widely known generalized inverse of a matrix
a matrix, but sometimes applied to other elements of algebraic structures which share some but not all properties expected for an inverse element. A
Moore–Penrose_inverse
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
Fundamental mechanical principles
variations in the transition amplitudes (qf|qi) to variations in an action matrix element: δ ( q r f | q r i ) = i ( q r f | δ S | q r i ) , {\displaystyle \delta
Action_principles
Physical interaction between magnetic moments
between the nuclei i and j, Ii is the nuclear spin of atom i, Δkmkm is a matrix element that represents the strength of the hyperfine interaction, m* is the
RKKY_interaction
Topics referred to by the same term
Look up Matrix, matrix, matrixes, or matrices in Wiktionary, the free dictionary. Matrix (pl.: matrices or matrixes) or MATRIX may refer to: Matrix (mathematics)
Matrix
Requirement that quantum states' time evolution operators are unitary transformations
imaginary part of the S-matrix. In order to see what the right-hand side is, let us look at any specific element of this matrix, e.g. between some initial
Unitarity
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
Concept in computer vision
In computer vision, the essential matrix is a 3 × 3 {\displaystyle 3\times 3} matrix, E {\displaystyle \mathbf {E} } that relates corresponding points
Essential_matrix
parity change Electric dipole transitions only have a non-vanishing matrix element between quantum states with different parity. Magnetic dipole transitions
Magnetic_dipole_transition
Algebraic element satisfying some of the criteria of an inverse
generalized inverse (or, g-inverse) of an element x is an element y that has some properties of an inverse element but not necessarily all of them. The purpose
Generalized_inverse
Stochastic matrix representing links between entities
Assuming there are N pages, we can fill out A by doing the following: A matrix element A i , j {\displaystyle A_{i,j}} is filled with 1 if node j {\displaystyle
Google_matrix
Theorem in quantum chemistry
computational complexity. Mathematically, the theorem states that the matrix element of the Hamiltonian H ^ {\displaystyle {\hat {H}}} between the ground
Brillouin's_theorem
Form of non-volatile memory used in computers and other electronic devices
360/30. Transformer matrix ROM achieves higher density storage than diode, resistor, or capacitor matrix ROMs, by using each matrix element to store multiple
Read-only_memory
Spectroscopic selection rule
integrand will be odd. Integrating over all space will then cause the matrix element to vanish, giving us the Laporte rule. They key assumption in deriving
Laporte_rule
Lowest energy state in quantum chromodynamics
otherwise the vacuum wouldn't be Lorentz invariant. By index matching, the matrix element must be J μ | 0 ⟩ = k μ | π ⟩ , {\displaystyle J_{\mu }|0\rangle =k_{\mu
QCD_vacuum
Formulation of quantum mechanics
this quantity and changing basis from p to q at each step allows the matrix element of H to be expressed as a simple function along each path. This function
Path-integral_formulation
Function approximating net physical effect
of the nucleon. However, the generic Lorentz-invariant form of the matrix element for the electromagnetic current interaction is known, ε μ N ¯ ( α (
Form factor (quantum field theory)
Form_factor_(quantum_field_theory)
Theorized type of radioactive decay
| 2 {\displaystyle \ \left|M^{0\nu }\right|^{2}\ } the (squared) matrix element of this nuclear decay process (according to the Feynman diagram), and
Neutrinoless double beta decay
Neutrinoless_double_beta_decay
Matrix equal to its transpose
each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative. In linear algebra, a real symmetric matrix represents a
Symmetric_matrix
Mathematical approach to quantum physics
the other energy eigenstates k ≠ n. Each term is proportional to the matrix element ⟨ k ( 0 ) | V | n ( 0 ) ⟩ {\displaystyle \langle k^{(0)}|V|n^{(0)}\rangle
Perturbation theory (quantum mechanics)
Perturbation_theory_(quantum_mechanics)
Change of an electron between energy levels within an atom
{r}}\cdot {\hat {\textbf {e}}}_{\mathrm {rad} }|1\rangle |^{2}} The dipole matrix element can be decomposed into the product of the radial integral and the angular
Atomic_electron_transition
Numerical linear algebra algorithm
off-diagonal element with the largest absolute value, called the pivot. The Jacobi eigenvalue method repeatedly performs rotations until the matrix becomes
Jacobi_eigenvalue_algorithm
Square matrix with ones on the main diagonal and zeros elsewhere
multiplicative identity of the matrix ring of all n × n {\displaystyle n\times n} matrices, and as the identity element of the general linear group G L
Identity_matrix
Application of computational physics
predicted particles. II Matrix element code generation: Various methods are used to automatically produce the matrix element expression in a computer
Automatic calculation of particle interaction or decay
Automatic_calculation_of_particle_interaction_or_decay
Types of energy range in a solid where no electron states can exist
frequency ν {\displaystyle \nu } x v c {\displaystyle x_{vc}} is a "matrix element", with units of length and typical value the same order of magnitude
Direct_and_indirect_band_gaps
Dimensionless quantity in spectroscopy
because in confined systems such as atoms or molecules the diagonal matrix element ⟨ n | p x | n ⟩ = 0 {\displaystyle \langle n|p_{x}|n\rangle =0} due
Oscillator_strength
scattering matrix element S f i = ⟨ f | S | i ⟩ , {\displaystyle S_{fi}=\langle f|S|i\rangle \;,} where S {\displaystyle S} is the S-matrix. The electron-positron
Initial and final state radiation
Initial_and_final_state_radiation
Approach to quantum theory
\sigma _{1}} and σ 2 {\displaystyle \sigma _{2}} is determined by the matrix element of the variation of the action operator: δ ⟨ σ 2 | σ 1 ⟩ = i ⟨ σ 2 |
Schwinger's quantum action principle
Schwinger's_quantum_action_principle
Linear algebra matrix
algebra, a circulant matrix is a square matrix in which all rows are composed of the same elements and each row is rotated one element to the right relative
Circulant_matrix
Matrix used to describe the transitions of a Markov chain
It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix. The stochastic matrix was first developed by Andrey Markov
Stochastic_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
Matrix whose entries are all 0
In mathematics, particularly linear algebra, a zero matrix or null matrix is a matrix all of whose entries are zero. It also serves as the additive identity
Zero_matrix
List of values for comparison
described by the decision matrix which has N rows and M columns, or M × N elements, as shown in the following table. Each element, such as Xij, is either
Decision_matrix
Numerical method used in structural mechanics
of the finite element method can be traced to the matrix analysis of structures where the concept of a displacement or stiffness matrix approach was introduced
Finite element method in structural mechanics
Finite_element_method_in_structural_mechanics
Chemical element with atomic number 80 (Hg)
Mercury is a chemical element; it has symbol Hg and atomic number 80. It is commonly known as quicksilver. A heavy, silvery d-block element, mercury is the
Mercury_(element)
Matrices similar to diagonal matrices
if there exists an n × n {\displaystyle n\times n} invertible matrix (i.e. an element of the general linear group GL ( n , F ) {\displaystyle \operatorname
Diagonalizable_matrix
Fundamental physical law of electromagnetism
scattering off that potential. Using the Feynman rules to compute the S-matrix element, we obtain in the non-relativistic limit with m 0 ≫ | p | {\displaystyle
Coulomb's_law
Geometric object that has length and direction
This matrix equation relates the scalar components of a in the n basis (u,v, and w) with those in the e basis (p, q, and r). Each matrix element cjk is
Euclidean_vector
Collection of objects, associated with an index set
consider the matrix A = [ 1 1 1 1 ] . {\displaystyle A={\begin{bmatrix}1&1\\1&1\end{bmatrix}}.} The set of the rows consists of a single element ( 1 , 1 )
Indexed_family
Spontaneous breakdown of an unstable subatomic particle into other particles
states (see below), M {\displaystyle {\mathcal {M}}\,} is the invariant matrix element or amplitude connecting the initial state to the final state (usually
Particle_decay
Specific element of an algebraic structure
mathematics, an identity element or neutral element of a binary operation is an element that leaves unchanged every element when the operation is applied
Identity_element
MATRIX ELEMENT
MATRIX ELEMENT
Female
English
Pet form of English Matilda, MATTIE means "mighty in battle." Compare with masculine Mattie.
Male
French
 French form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Female
Finnish
Pet form of Finnish Katariina, KATRI means "pure."
Female
Finnish
Finnish form of Greek Margarites, MAARIT means "pearl."
Girl/Female
Arabic, Australian, Basque, French, Latin
Lady; Feminine of Martin; Warlike
Male
English
 English form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Female
Finnish
Finnish form of Greek Maria, MAARIA means "obstinacy, rebelliousness" or "their rebellion."Â
Male
English
Pet form of English Martin, MARTIE means "of/like Mars."
Female
German
Pet form of German Katarine, KATRIN means "pure."
Girl/Female
Maori
The Maori form of April.
Male
Italian
Italian form of Hebrew Mattithyah, MATTIA means "gift of God."
Male
English
Pet form of English Matthew, MATTIE means "gift of God." Compare with feminine Mattie.
Female
English
English form of Latin Viatrix, BEATRIX means "voyager (through life)."
Male
English
Anglicized form of Irish Gaelic MainchÃn, MANNIX means "little monk."
Male
French
French and German form of Greek Mattathias, MATHIS means "gift of God."
Girl/Female
Biblical
Rain, prison.
Female
Welsh
Welsh form of Old French Caterine, CATRIN means "pure."
Male
Hungarian
Czech and Hungarian form of Greek Patrikios, PATRIK means "patrician, of noble descent."
Surname or Lastname
English (of Welsh origin)
English (of Welsh origin) : variant of Maddox.
Female
English
French form of Latin Maria, MARIE means "obstinacy, rebelliousness" or "their rebellion."
MATRIX ELEMENT
MATRIX ELEMENT
Male
French
Variant spelling of French Ferrand, FERRANT means "ardent for peace."
Boy/Male
Hindu
New, Rainy, Handsome, Gratified
Boy/Male
Biblical
Passing over, testimony of the Lord.
Boy/Male
Czechoslovakian
Goat.
Girl/Female
Hindu, Indian, Marathi, Sanskrit
Pleasant; Delighted
Girl/Female
Arabic
Pure; Grace; Continuous; Day; No Darkness
Boy/Male
Indian
King
Male
English
Anglicized form of Hebrew Zakkay, ZACCAI means "clean, innocent." In the bible, this is the name of the head of a family of Babylonian Exile returnees.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Kashmiri, Malayalam, Marathi, Punjabi, Sanskrit, Sikh, Tamil, Traditional
Power
Surname or Lastname
English (Norfolk)
English (Norfolk) : probably from Middle English milk ‘milk’, applied as a metonymic occupational name for a producer or seller of milk.In some instances, probably a translation of German Milch, a variant of Slavic Milich or of Dutch Mielke (a pet form of Miele), or a shortening of Slavic Milkovich.
MATRIX ELEMENT
MATRIX ELEMENT
MATRIX ELEMENT
MATRIX ELEMENT
MATRIX ELEMENT
n.
The womb.
n.
The five simple colors, black, white, blue, red, and yellow, of which all the rest are composed.
n.
See Matrix.
n.
The cavity in which anything is formed, and which gives it shape; a die; a mold, as for the face of a type.
pl.
of Maori
n.
The martin.
n.
A housekeeper; esp., a woman who manages the domestic economy of a public instution; a head nurse in a hospital; as, the matron of a school or hospital.
n.
A genus of swallows including the purple martin. See Martin.
v. i.
The mineral substance which incloses a vein; a matrix; a gangue.
n.
Hence, that which gives form or origin to anything
v. t.
The white fibrous matter forming the matrix from which fungi.
n.
A rectangular arrangement of symbols in rows and columns. The symbols may express quantities or operations.
pl.
of Matrix
n.
The earthy or stony substance in which metallic ores or crystallized minerals are found; the gangue.
n.
A mold; a matrix.
n.
The lifeless portion of tissue, either animal or vegetable, situated between the cells; the intercellular substance.
n.
In type founding and forging, an impression or matrix, formed by a punch drift.
a.
Of or pertaining to the Maoris or to their language.
a.
Of or pertaining to the meter as a standard of measurement; of or pertaining to the decimal system of measurement of which a meter is the unit; as, the metric system; a metric measurement.