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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
Matrix whose entries are the coefficients of a linear equation
linear algebra, a coefficient matrix is a matrix consisting of the coefficients of the variables in a set of linear equations. The matrix is used in solving
Coefficient_matrix
Measure of linear correlation
statistics, the Pearson correlation coefficient (PCC), also known as Pearson's r, the Pearson product-moment correlation coefficient (PPMCC), or simply the unqualified
Pearson correlation coefficient
Pearson_correlation_coefficient
Table layout for visualizing performance; also called an error matrix
evaluate a confusion matrix is the Matthews correlation coefficient (MCC). Other metrics can be included in a confusion matrix, each of them having their
Confusion_matrix
Algorithmic runtime requirements for matrix multiplication
complexity of matrix multiplication depends on the arithmetic domain of the matrix coefficient. For finite fields the bit length of the coefficients can be bounded
Computational complexity of matrix multiplication
Computational_complexity_of_matrix_multiplication
Basic result in harmonic analysis on compact topological groups
group. The theorem has three parts. The first part states that the matrix coefficients of irreducible representations of G are dense in the space C(G) of
Peter–Weyl_theorem
Multiplicative factor in a mathematical expression
§ Leading term, coefficient and monomial. In linear algebra, a system of linear equations is frequently represented by its coefficient matrix. For example
Coefficient
Square matrices satisfy their characteristic equation
n\times n} matrix M, the transpose of its cofactor matrix. This is a matrix whose coefficients are given by polynomial expressions in the coefficients of M
Cayley–Hamilton_theorem
Statistical relationship
of correlation used are product-moment coefficients, the correlation matrix is the same as the covariance matrix of the standardized random variables X
Correlation
Statistical measure of association for two binary variables
In statistics, the phi coefficient, also known as the mean square contingency coefficient or Yule coefficient of correlation and commonly denoted by φ
Phi_coefficient
Indicator for how well data points fit a line or curve
In statistics, the coefficient of determination, denoted R2 or r2 and pronounced "R squared", is the proportion of the variation in the dependent variable
Coefficient_of_determination
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
Matrix formed by appending columns of two other matrices
if the rank of the augmented matrix ( A | B ) {\displaystyle (A\vert B)} is greater than the rank of the coefficient matrix A {\displaystyle A} . If, on
Augmented_matrix
Formulation of quantum mechanics
the lowest frequency, and the matrix element Amn is the (m − n)th Fourier coefficient of the classical orbit, the matrix for A is nonzero only on the
Matrix_mechanics
Polynomial whose roots are the eigenvalues of a matrix
eigenvalues as roots. It has the determinant and the trace of the matrix among its coefficients. The characteristic polynomial of an endomorphism of a finite-dimensional
Characteristic_polynomial
Formula for systems of linear equations
expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the column
Cramer's_rule
Nonparametric measure of rank correlation
In statistics, Spearman's rank correlation coefficient or Spearman's ρ is a number ranging from -1 to 1 that indicates how strongly two sets of ranks
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Numerical measure of a statistical relationship between variables
A correlation coefficient is a numerical measure of some type of linear correlation, meaning a linear function between two variables. The variables may
Correlation_coefficient
Topics referred to by the same term
linear operator (especially a modified Hamiltonian) in quantum theory Matrix coefficient, a type of function in representation theory Element (software), free
Matrix_element
Matrix which differs from the identity matrix by one elementary row operation
&\\&&&&&&1\end{bmatrix}}} So Ti,j A is the matrix produced by exchanging row i and row j of A. Coefficient wise, the matrix Ti,j is defined by : [ T i , j ] k
Elementary_matrix
Measure of how connected and clustered a node is in its graph
Since any graph is fully specified by its adjacency matrix A, the local clustering coefficient for a simple undirected graph can be expressed in terms
Clustering_coefficient
Matrix used to study systems of ordinary differential equations
equations (ODEs), a monodromy matrix is the fundamental matrix of a system of ODEs evaluated at the period of the coefficients of the system. It is used for
Monodromy_matrix
Tendency of matter to change volume in response to a change in temperature
strain) divided by the change in temperature is called the material's coefficient of linear thermal expansion. For small temperature changes, this is nearly
Thermal_expansion
Mathematical method used in optics and acoustics
involves converting the system matrix back into reflection and transmission coefficients. Below is described how the transfer matrix is applied to electromagnetic
Transfer-matrix method (optics)
Transfer-matrix_method_(optics)
Matrix whose only nonzero elements are on its main diagonal
As explained in determining coefficients of operator matrix, there is a special basis, e1, ..., en, for which the matrix A takes the diagonal form. Hence
Diagonal_matrix
Matrix of geometric progressions
a=V^{-1}y} . That is, the map from coefficients to values of polynomials is a bijective linear mapping with matrix V, and the interpolation problem has
Vandermonde_matrix
In mathematics, invariant of square matrices
Determinants occur throughout mathematics. For example, a matrix is often used to represent the coefficients in a system of linear equations, and determinants
Determinant
Two-dimensional matrix barcode
, which may also be written in the form of a matrix of decimal coefficients: [1 242 100 178 97 213 142 42 61 91 158 153 41] The 12-byte
Data_Matrix
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
Integer matrices with +1 or −1 determinant; invertible over the integers. GL_n(Z)
incidence matrix of a bipartite graph, which is the coefficient matrix for bipartite matching, is totally unimodular (TU). (The unoriented incidence matrix of
Unimodular_matrix
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
Video and image technology for HDR displays
(CICP) are used to signal the transfer function, color primaries and matrix coefficients. It is defined in both ITU-T H.273 and ISO/IEC 23091-2. It is used
High-dynamic-range_television
Method for approximating eigenvalues
} For a non-trivial solution of c, we require determinant of the matrix coefficient of c to be zero. det ( K − ω 2 M ) = 0 {\displaystyle \det(K-\omega
Rayleigh–Ritz_method
a matrix. The major approaches within statistical multivariate data analysis can all be brought into a common framework in which the RV coefficient is
RV_coefficient
Universal construction of a complex Lie group from a real Lie group
characters of the Hopf algebra of representative functions, i.e. the matrix coefficients of finite-dimensional representations of the group. In any finite-dimensional
Complexification_(Lie_group)
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
Widely used NTSC television test pattern
(1.00 * 219 + 16 = 235) using BT.709 matrix coefficients (only white and black are the same using BT.601 matrix), taken from the standard: ITU-R Rec.
SMPTE_color_bars
Array of numbers
the matrix of coefficients of the highest-order differential operators of the equation. For elliptic partial differential equations this matrix is positive
Matrix_(mathematics)
Table that displays the frequency of variables
(also known as a cross tabulation or crosstab) is a type of table in a matrix format that displays the multivariate frequency distribution of the variables
Contingency_table
Concept in probability theory and statistics
relationship between two variables of interest, using their correlation coefficient will give misleading results if there is another confounding variable
Partial_correlation
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
In probability theory and statistics, the coefficient of variation (CV), also known as normalized root-mean-square deviation (NRMSD), and relative standard
Coefficient_of_variation
Number of subsets of a given size
the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by
Binomial_coefficient
Statistical concept
themselves, the inverse of the correlation matrix R x x {\displaystyle R_{xx}} accounts for this. The squared coefficient of multiple correlation can also be
Coefficient of multiple correlation
Coefficient_of_multiple_correlation
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
polynomial matrix. A QEP is said to be regular if det ( Q ( λ ) ) ≢ 0 {\displaystyle {\text{det}}(Q(\lambda ))\not \equiv 0} identically. The coefficient of the
Quadratic_eigenvalue_problem
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
Statistic measuring inter-rater agreement for categorical items
Cohen's kappa coefficient (symbol κ, lowercase Greek kappa) is a statistic used to measure inter-rater reliability for qualitative or categorical data
Cohen's_kappa
Possible form of a matrix
in a column below a leading coefficient are zeros. The following is an example of a 4 × 5 {\displaystyle 4\times 5} matrix in row echelon form, but not
Row_echelon_form
as the dimensional wear coefficient or the specific wear rate. This is usually quoted in units of mm3 N−1 m−1. As metal matrix composite (MMC) materials
Wear_coefficient
Dimension of the column space of a matrix
is inconsistent if the rank of the augmented matrix is greater than the rank of the coefficient matrix. If on the other hand, the ranks of these two
Rank_(linear_algebra)
Square matrix without an inverse
invertibility of the coefficient matrix A {\displaystyle A} ensures the algorithm produces a unique solution. For example, when matrix is invertible the
Singular_matrix
Rational mathematical function indexed by integer partitions
integers that can be used to calculate integrals of products of matrix coefficients over classical groups. They were first studied by Weingarten (1978)
Weingarten_function
Matrix used to analyze the stability of a polynomial by its coefficients
Routh–Hurwitz matrix, or more commonly just Hurwitz matrix, corresponding to a polynomial is a particular matrix whose nonzero entries are coefficients of the
Routh–Hurwitz_matrix
representation of a Lie group G is said to be in the discrete series if the matrix coefficients of it are all square integrable. For example, if G is compact, then
Glossary of representation theory
Glossary_of_representation_theory
Matrix representing the effect of scattering on a physical system
Structure". In this paper Wheeler introduced a scattering matrix – a unitary matrix of coefficients connecting "the asymptotic behaviour of an arbitrary particular
S-matrix
Method for model fitting in statistics
generalized least squares, when all the off-diagonal entries of the covariance matrix of the errors are null. The fit of a model to a data point is measured by
Weighted_least_squares
Type of representation of a linear semisimple Lie group
matrix coefficients lie in the Lp space L2+ε(G) for any ε > 0. This condition, as just given, is slightly weaker than the condition that the matrix coefficients
Tempered_representation
arises as the matrix coefficient of a K-invariant vector in an irreducible representation of G. The key examples are the matrix coefficients of the spherical
Zonal_spherical_function
Correlation of a signal with a time-shifted copy of itself, as a function of shift
autocovariance function to get a time-dependent Pearson correlation coefficient. However, in other disciplines (e.g. engineering) the normalization is
Autocorrelation
Measure of wave reflectivity
In physics and electrical engineering the reflection coefficient is a parameter that describes how much of a wave is reflected by an impedance discontinuity
Reflection_coefficient
Formula for the derivative of a matrix determinant
In matrix calculus, Jacobi's formula expresses the derivative of the determinant of a matrix A in terms of the adjugate of A and the derivative of A.
Jacobi's_formula
Symbolic representation of a chemical reaction
also be written using an efficient matrix formalism. First, to unify the reactant and product stoichiometric coefficients sj, let us introduce the quantity
Chemical_equation
Similarity measure for number sequences
Other names for cosine similarity include Orchini similarity and Tucker coefficient of congruence; the Otsuka–Ochiai similarity (see below) is cosine similarity
Cosine_similarity
Theorem in linear algebra
spectral radius ρ ( A ) {\displaystyle \rho (A)} is equal to r. If the matrix coefficients are algebraic, this implies that the eigenvalue is a Perron number
Perron–Frobenius_theorem
Theorem of matrix algebra of invariance properties under basis transformations
Sylvester's law of inertia is a theorem in matrix algebra about certain properties of the coefficient matrix of a real quadratic form that remain invariant
Sylvester's_law_of_inertia
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
Calculation of relative masses of reactants and products in chemical reactions
the product has 2 hydrogen and 3 oxygen. To balance the hydrogen, a coefficient of 2 is added to the product H2O, and to fix the imbalance of oxygen
Stoichiometry
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
Sums in quantum mathematics
of this tetrahedron. In representation theory, 6-j symbols are matrix coefficients of the associator isomorphism in a tensor category. For example,
6-j_symbol
Statistical technique used to examine construct validity
prototypical matrix and what the correlations between measures mean. The diagonal line is typically filled in with a reliability coefficient of the measure
Multitrait-multimethod_matrix
Measure of similarity and diversity between sets
independently by Paul Jaccard, originally giving the French name coefficient de communauté (coefficient of community), and independently formulated again by Taffee
Jaccard_index
Vectors mapped to 0 by a linear map
closed subspace of V. Consider a linear map represented as a m × n matrix A with coefficients in a field K (typically R {\displaystyle \mathbb {R} } or C {\displaystyle
Kernel_(linear_algebra)
Algorithms for matrix decomposition
product matrix WH is a linear combination of the 10 column vectors in the features matrix W with coefficients supplied by the coefficients matrix H. This
Non-negative matrix factorization
Non-negative_matrix_factorization
Ratio of concentrations in a mixture at equilibrium
In the physical sciences, a partition coefficient (P) or distribution coefficient (D) is the ratio of concentrations of a compound in a mixture of two
Partition_coefficient
Specialized notation for multivariable calculus
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various
Matrix_calculus
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
Directed graph with no directed cycles
self-loops, its adjacency matrix must have a zero diagonal, so adding I preserves the property that all matrix coefficients are 0 or 1. A multitree (also
Directed_acyclic_graph
Representation theory
space A*/W. The spherical function φλ can be identified with the matrix coefficient of the spherical principal series of G. If M is the centraliser of
Plancherel theorem for spherical functions
Plancherel_theorem_for_spherical_functions
values in their coefficients. Concepts and topics studied within combinatorial matrix theory include: (0,1)-matrix, a matrix whose coefficients are all 0 or
Combinatorial_matrix_theory
Representation theory of the symplectic group
Gelfand–Naimark construction, the matrix coefficient of any vector determines the vector up to a scalar multiple. Since the matrix coefficients of F = E0 and f = H0
Oscillator_representation
process in which an initial permutation matrix is modified by repeatedly changing to one any matrix coefficient that has two or more orthogonal neighbors
Separable_permutation
Algorithm to smooth data points
The coefficients of y in these expressions are known as convolution coefficients. They are elements of the matrix C = ( J T J ) − 1 J
Savitzky–Golay_filter
Triangular array of the binomial coefficients
binomial coefficient Hockey-stick identity Leibniz harmonic triangle Multiplicities of entries in Pascal's triangle (Singmaster's conjecture) Pascal matrix Pascal's
Pascal's_triangle
Central object in linear algebra; mapping vectors to vectors
there exists an m × n {\displaystyle m\times n} matrix A {\displaystyle A} , called the transformation matrix of T {\displaystyle T} , such that: T ( x )
Transformation_matrix
purely combinatorial definition above, they can also be defined as the coefficients that arise when one expresses the Schur polynomial s λ {\displaystyle
Kostka_number
Bosons that mediate the weak interaction
{\displaystyle V_{ij}} denote the corresponding CKM matrix coefficients. Unitarity of the CKM matrix implies that | V ud | 2 + | V us | 2 + | V ub | 2
W_and_Z_bosons
Use of mathematical groups in magnetochemistry
matrices, with n = 2j + 1 and j ≥ 0. The matrix coefficients for each irreducible representation Vj form a set of matrix units. This direct sum decomposition
Finite_subgroups_of_SU(2)
Composite material consisting of fibers or particles in a metallic matrix
generated in the composite due to the mismatch between the coefficients of the metal matrix and fiber. The manufacturing residual stresses significantly
Metal_matrix_composite
Method for estimating the unknown parameters in a linear regression model
known as the moment matrix of regressand by regressors. Finally, β ^ {\displaystyle {\hat {\boldsymbol {\beta }}}} is the coefficient vector of the least-squares
Ordinary_least_squares
Measure of the joint variability
fluxes. The covariance matrix is used to capture the spectral variability of a signal. The Pearson product-moment correlation coefficient between two random
Covariance
Integral expressing the amount of overlap of one function as it is shifted over another
similar result holds for compact groups (not necessarily abelian): the matrix coefficients of finite-dimensional unitary representations form an orthonormal
Convolution
Number of solutions of linear systems in terms of matrix ranks
system of linear equations, given the ranks of its augmented matrix and coefficient matrix. The theorem is variously known as the: Rouché–Capelli theorem
Rouché–Capelli_theorem
Matrix with shifting rows
In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to
Toeplitz_matrix
Matrix used in finite element analysis
_{\Omega }\varphi _{i}f\,dx,} the coefficients ui are determined by the linear system Au = F. The stiffness matrix is symmetric, i.e. Aij = Aji, so all
Stiffness_matrix
Theorem about the dual of a Hilbert space
surjectivity of linear map to anti-dual Matrix coefficient – Functions on special groups related to their matrix representations Trèves 2006, pp. 112–123
Riesz_representation_theorem
Sum of elements on the main diagonal
nilpotent. The trace of an n × n {\displaystyle n\times n} matrix A {\displaystyle A} is the coefficient of t n − 1 {\displaystyle t^{n-1}} in the characteristic
Trace_(linear_algebra)
Statistical modeling method
explanatory variable with a slope coefficient. A multiple regression e right hand side, each with its own slope coefficient Rencher, Alvin C.; Christensen
Linear_regression
therefore be constant on the real axis with the origin removed. Thus the matrix coefficient ψ(x) = (xξ,ξ) satisfies ψ(g) = 1 for g in A · N. By unitarity, ||gξ
Ergodic_flow
Values which describe behavior of a linear electric circuit
Scattering parameters or S-parameters are the elements of a scattering matrix or S-matrix which describe the steady state response of linear electrical networks
Scattering_parameters
Matrix equal to its conjugate-transpose
by imaginary coefficients, which results in skew-Hermitian matrices. Here is another useful case of a Hermitian matrix. If a square matrix A {\displaystyle
Hermitian_matrix
MATRIX COEFFICIENT
MATRIX COEFFICIENT
Girl/Female
Arabic, Australian, Basque, French, Latin
Lady; Feminine of Martin; Warlike
Male
Italian
Italian form of Hebrew Mattithyah, MATTIA means "gift of God."
Male
Hungarian
Czech and Hungarian form of Greek Patrikios, PATRIK means "patrician, of noble descent."
Female
English
Pet form of English Matilda, MATTIE means "mighty in battle." Compare with masculine Mattie.
Girl/Female
Maori
The Maori form of April.
Male
English
Anglicized form of Irish Gaelic MainchÃn, MANNIX means "little monk."
Female
Finnish
Finnish form of Greek Maria, MAARIA means "obstinacy, rebelliousness" or "their rebellion."Â
Female
English
English form of Latin Viatrix, BEATRIX means "voyager (through life)."
Girl/Female
Biblical
Rain, prison.
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."
Female
Finnish
Pet form of Finnish Katariina, KATRI means "pure."
Male
English
 English form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Female
German
Pet form of German Katarine, KATRIN means "pure."
Male
French
 French form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Female
Welsh
Welsh form of Old French Caterine, CATRIN means "pure."
Female
Finnish
Finnish form of Greek Margarites, MAARIT means "pearl."
Male
French
French and German form of Greek Mattathias, MATHIS means "gift of God."
Male
English
Pet form of English Martin, MARTIE means "of/like Mars."
Male
English
Pet form of English Matthew, MATTIE means "gift of God." Compare with feminine Mattie.
MATRIX COEFFICIENT
MATRIX COEFFICIENT
Boy/Male
Muslim
Lover
Boy/Male
English American
Friend; good friend.
Boy/Male
Hindu, Indian
Target
Boy/Male
Indian
Intelligent
Girl/Female
English
or Agnes.
Boy/Male
Hindu, Indian, Marathi
A Great Warrior
Boy/Male
Indian
Invincible
Male
German
Variant spelling of Old German Hartmann, HARTMAN means "strong-man."
Boy/Male
Gujarati, Hindu, Indian, Kannada, Marathi, Sanskrit
Karna
Surname or Lastname
North German
North German : variant of Fick.English : variant of Fitch.
MATRIX COEFFICIENT
MATRIX COEFFICIENT
MATRIX COEFFICIENT
MATRIX COEFFICIENT
MATRIX COEFFICIENT
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.
pl.
of Maori
pl.
of Matrix
n.
The lifeless portion of tissue, either animal or vegetable, situated between the cells; the intercellular substance.
n.
A rectangular arrangement of symbols in rows and columns. The symbols may express quantities or operations.
v. t.
The white fibrous matter forming the matrix from which fungi.
n.
The womb.
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.
a.
Of or pertaining to the Maoris or to their language.
n.
Hence, that which gives form or origin to anything
v. i.
The mineral substance which incloses a vein; a matrix; a gangue.
n.
A mold; a matrix.
n.
The five simple colors, black, white, blue, red, and yellow, of which all the rest are composed.
n.
In type founding and forging, an impression or matrix, formed by a punch drift.
n.
The earthy or stony substance in which metallic ores or crystallized minerals are found; the gangue.
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.
n.
The martin.