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Technique for computing light scattering by nonspherical particles
The transition matrix method (T-matrix method or TMM) is a computational technique of light scattering by nonspherical particles originally formulated
T-matrix_method
A {\displaystyle A^{-1}A} is the identity matrix. There are many methods for calculating an inverse matrix, if it exists. Gaussian elimination is a useful
Methods_of_matrix_inversion
out, using either a stiffness matrix or a flexibility matrix. Direct stiffness method Flexibility method "MATRIX METHODS OF STRUCTURAL ANALYSIS - NATO
Matrix_method
Mathematical method used in optics and acoustics
The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic or acoustic waves through a stratified
Transfer-matrix method (optics)
Transfer-matrix_method_(optics)
Pugh concept selection
The decision-matrix method, also Pugh method or Pugh concept selection, invented by Stuart Pugh, is a qualitative technique used to rank the multi-dimensional
Decision-matrix_method
Scattering of light by tiny particles in a colloidal suspension
Light scattering by particles of complex shape are described by the T-matrix method. Fog scattering traffic light The colloid on the right shows Tyndall
Tyndall_effect
Matrix decomposition
is a factorization of a matrix A {\displaystyle A} into a canonical form given by A = V D V T {\displaystyle A=VDV^{\mathsf {T}}} , where D {\displaystyle
Eigendecomposition of a matrix
Eigendecomposition_of_a_matrix
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
a matrix-free method is an algorithm for solving a linear system of equations or an eigenvalue problem that does not store the coefficient matrix explicitly
Matrix-free_methods
electromagnetics, the scattering-matrix method (SMM) is a numerical method used to solve Maxwell's equations, related to the transfer-matrix method. SMM can, for example
Scattering-matrix_method
American atmospheric scientist (1959–2020)
Institute for Space Studies. He is best known for his contributions to the T-matrix method for the computation of light scattering by complex particles and clusters
Michael_I._Mishchenko
Mathematical optimization algorithm
conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-semidefinite
Conjugate_gradient_method
Method of computing electromagnetic fields
The transmission-line matrix (TLM) method is a space and time discretising method for computation of electromagnetic fields. It is based on the analogy
Transmission-line matrix method
Transmission-line_matrix_method
Real square matrix whose columns and rows are orthogonal unit vectors
orthogonal matrix or orthonormal matrix Q, is a real-valued square matrix whose columns and rows are orthonormal vectors. One way to express this is Q T Q =
Orthogonal_matrix
Matrices similar to diagonal matrices
linear algebra, a square matrix A {\displaystyle A} is called diagonalizable or non-defective if it is similar to a diagonal matrix. That is, if there exists
Diagonalizable_matrix
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
H-matrix is a matrix whose comparison matrix is an M-matrix. It is useful in iterative methods. Definition: Let A = (aij) be a n × n complex matrix. Then
H-matrix_(iterative_method)
Optimization algorithm
method, except using approximations of the derivatives of the functions in place of exact derivatives. Newton's method requires the Jacobian matrix of
Quasi-Newton_method
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
Iterative method used to solve a linear system of equations
a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi. Let A x = b
Jacobi_method
Iterative method used to solve a linear system of equations
algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system
Gauss–Seidel_method
scattering T-matrix as a functional depending on two unknown wave functions. The functional attains stationary value equal to actual scattering T-matrix. The
Schwinger variational principle
Schwinger_variational_principle
Algorithms for matrix decomposition
Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra
Non-negative matrix factorization
Non-negative_matrix_factorization
Method of analysis in probability theory
the matrix geometric method is a method for the analysis of quasi-birth–death processes, continuous-time Markov chain whose transition rate matrix has
Matrix_geometric_method
Representation of a matrix as a sum
linear algebra, a matrix splitting is an expression which represents a given matrix as a sum or difference of matrices. Many iterative methods (for example
Matrix_splitting
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
American mathematician and physicist (1928–2012)
and acoustics. He has introduced the extended boundary condition and T-matrix methods, widely used in the analysis of scattering in complex structures. Peter
Peter_C._Waterman
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)
Approximations used in machine learning
Low-rank matrix approximations are essential tools in the application of kernel methods to large-scale learning problems. Kernel methods (for instance
Low-rank matrix approximations
Low-rank_matrix_approximations
Matrix used in finite element analysis
the finite element method for the numerical solution of elliptic partial differential equations, the stiffness matrix is a matrix that represents the
Stiffness_matrix
Computing technique in probability theory
In probability theory, the matrix analytic method is a technique to compute the stationary probability distribution of a Markov chain which has a repeating
Matrix_analytic_method
Scattering of an electromagnetic plane wave by a sphere
that allows a treatment of more generally shaped particles is the T-matrix method, which also relies on a series approximation to solutions of Maxwell's
Mie_scattering
Quasi-Newton root-finding method for the multivariable case
the one-dimensional Newton's method, replacing the derivative with an approximate Jacobian J. The approximate Jacobian matrix is determined iteratively based
Broyden's_method
Regularization technique for ill-posed problems
another regularization method in statistics. Elastic net regularization Matrix regularization L-curve In statistics, the method is known as ridge regression
Ridge_regression
Method for numerical solution of certain systems of equations
the MINRES method due to Paige and Saunders in 1975. The MINRES method requires the matrix to be symmetric, but has the advantage that it only requires handling
Generalized minimal residual method
Generalized_minimal_residual_method
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
Central object in linear algebra; mapping vectors to vectors
m\times n} matrix A {\displaystyle A} , called the transformation matrix of T {\displaystyle T} , such that: T ( x ) = A x {\displaystyle T(\mathbf {x}
Transformation_matrix
Planning time spent on specific activities
urgent/not urgent, and then placed in according quadrants in an Eisenhower matrix. Tasks in the quadrants are then handled as follows. Important/Urgent quadrant
Time_management
Matrix that converges to zero matrix
in a convergent matrix T. A semi-convergent splitting of a matrix A results in a semi-convergent matrix T. A general iterative method converges for every
Convergent_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
Statistical NM-method
tables. The method finds the matrix X {\displaystyle X} ( X ∈ R n × m {\displaystyle X\in \mathbb {R} ^{n\times m}} ) which is "closest" to matrix Z {\displaystyle
NM-method
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
Matrix representation of a graph
negative continuous Laplacian obtained by the finite difference method. The Laplacian matrix relates to many functional graph properties. Kirchhoff's theorem
Laplacian_matrix
Numerical method
adjoint matrix A ∗ = A ¯ T {\displaystyle A^{*}={\overline {A}}^{T}} is used. When the initial problem consists of calculating the product s T x {\displaystyle
Adjoint_state_method
Optimization method
Hessian matrix of the loss function, obtained only from gradient evaluations (or approximate gradient evaluations) via a generalized secant method. Since
Broyden–Fletcher–Goldfarb–Shanno algorithm
Broyden–Fletcher–Goldfarb–Shanno_algorithm
Iterative method for solving the Sylvester matrix equations
implicit (ADI) method is an iterative method used to solve Sylvester matrix equations. It is a popular method for solving the large matrix equations that
Alternating-direction implicit method
Alternating-direction_implicit_method
Mathematical operation
square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if the matrix product BB is
Square_root_of_a_matrix
Linear programming algorithm
of the matrix representing the constraints. The matrix-oriented approach allows for greater computational efficiency by enabling sparse matrix operations
Revised_simplex_method
Algorithm for solving systems of linear equations
corresponding matrix of coefficients. This method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse
Gaussian_elimination
Numerical approximation algorithm
^{k}\quad \forall k\geq 0} and this matrix is called the iteration matrix. An iterative method with a given iteration matrix C {\displaystyle C} is called convergent
Iterative_method
Matrix decomposition method
decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for
Cholesky_decomposition
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
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
Calculation of relative masses of reactants and products in chemical reactions
Arreckx, Sylvain; Fleming, Ronan M.T. (August 2020). "Structural conserved moiety splitting of a stoichiometric matrix". Journal of Theoretical Biology
Stoichiometry
Multivariable generalization of the Student's t-distribution
the matrix t-distribution is distinct and makes particular use of the matrix structure. One common method of construction of a multivariate t-distribution
Multivariate_t-distribution
Polynomial Matrix Spectral Factorization or Matrix Fejér–Riesz Theorem is a tool used to study the matrix decomposition of polynomial matrices. Polynomial
Polynomial matrix spectral factorization
Polynomial_matrix_spectral_factorization
computation time compared to finite difference methods. To accomplish this, a fractional differentiation matrix is derived at the Chebyshev Gauss–Lobatto collocation
Fractional Chebyshev collocation method
Fractional_Chebyshev_collocation_method
Property of a mathematical matrix
symmetric matrix M {\displaystyle M} with real entries is positive-definite if the real number x T M x {\displaystyle \mathbf {x} ^{\mathsf {T}}M\mathbf
Definite_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
Numerical linear algebra algorithm
eigenvalue algorithm is an iterative method for the calculation of the eigenvalues and eigenvectors of a real symmetric matrix (a process known as diagonalization)
Jacobi_eigenvalue_algorithm
Class of algorithms for pattern analysis
processes, then the Gram matrix K {\displaystyle \mathbf {K} } can also be called a covariance matrix. Application areas of kernel methods are diverse and include
Kernel_method
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
Concepts from linear algebra
iterative method to compute eigenvalues and eigenvectors, among several other possibilities. Most numeric methods that compute the eigenvalues of a matrix also
Eigenvalues_and_eigenvectors
Method for approximating eigenvalues
Rayleigh–Ritz method is commonly applied to approximate an eigenvalue problem A x = λ x {\displaystyle A\mathbf {x} =\lambda \mathbf {x} } for the matrix A ∈ C
Rayleigh–Ritz_method
Wilson's normal mode analysis
the method is called the GF method, often with the name of its originator attached to it: Wilson's GF method. By matrix transposition in both sides of
GF_method
Parameter estimation technique in statistics, particularly econometrics
outlined method is that we cannot take W = Ω−1 because, by the definition of matrix Ω, we need to know the value of θ0 in order to compute this matrix, and
Generalized_method_of_moments
Mathematical algorithm
conventional matrix equation of form A x = b {\displaystyle A\mathbf {x} =\mathbf {b} } , which can then be solved in a variety of methods (see Notes)
Gauss–Newton_algorithm
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
Signal processing technique
Generalized pencil-of-function method (GPOF), also known as matrix pencil method, is a signal processing technique for estimating a signal or extracting
Generalized pencil-of-function method
Generalized_pencil-of-function_method
Mathematical concept
symplectic matrix is a 2 n × 2 n {\displaystyle 2n\times 2n} matrix M {\displaystyle M} with real entries that satisfies the condition where M T {\displaystyle
Symplectic_matrix
In mathematics, invariant of square matrices
square matrix. The determinant of a matrix A is commonly denoted det(A), det A, or |A|. Its value characterizes some properties of the matrix and the
Determinant
Computational simulation method for open quantum systems
on the wave function rather than using a density matrix approach. The main component of this method is evolving the system's wave function in time with
Quantum_jump_method
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
Concept in differential equation mathematics
u n + Δ t u ˙ n + 1 2 Δ t 2 u ¨ β {\displaystyle u_{n+1}=u_{n}+\Delta t~{\dot {u}}_{n}+{\begin{matrix}{\frac {1}{2}}\end{matrix}}\Delta t^{2}~{\ddot
Newmark-beta_method
Matrix in which most of the elements are zero
direct methods exist for sparse matrix solving. Iterative methods, such as conjugate gradient method and GMRES utilize fast computations of matrix-vector
Sparse_matrix
Hurwitz-stable matrix P-matrix Perron–Frobenius theorem Z-matrix L-matrix M-matrix H-matrix (iterative method) Varga, Richard S. (2006). "Basic Iterative Methods and
Comparison_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
Numerical method for non-linear problems
includes a Jacobian matrix. Solving this directly would involve calculation of the Jacobian's inverse, when the Jacobian matrix itself is often difficult
Newton–Krylov_method
Mathematical procedure
the user-item interaction matrix into the product of two lower dimensionality rectangular matrices. This family of methods became widely known during
Matrix factorization (recommender systems)
Matrix_factorization_(recommender_systems)
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
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
consisting of the 3x3 rotation matrix R and the 1x3 translation vector p. The matrix is augmented to create a 4x4 square matrix. g s t ( 0 ) = [ R p 0 1 ] {\displaystyle
Product of exponentials formula
Product_of_exponentials_formula
Process of estimating the parameters of a pinhole camera model
coordinates is C = − R − 1 T = − R T T {\displaystyle C=-R^{-1}T=-R^{T}T} (since R {\displaystyle R} is a rotation matrix). This can be verified by checking
Camera_resectioning
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
Evolutionary algorithm
are represented by a covariance matrix. The covariance matrix adaptation (CMA) is a method to update the covariance matrix of this distribution. This is
CMA-ES
Computer printing process
or NLQ), usually at the cost of speed. Dot matrix printing is typically distinguished from non-impact methods, such as inkjet, thermal, or laser printing
Dot_matrix_printing
Academic journal
The SIAM Journal on Matrix Analysis and Applications is a peer-reviewed scientific journal covering matrix analysis and its applications. The relevant
SIAM Journal on Matrix Analysis and Applications
SIAM_Journal_on_Matrix_Analysis_and_Applications
Approximation method
{\mathcal {G}}[u](x)=\int _{\Omega }\kappa (x,y)u(y)\,dy.} The Galerkin method leads to matrix entries of the form g i j = ∫ Ω ∫ Ω κ ( x , y ) φ i ( x ) ψ j (
Hierarchical_matrix
Optimization algorithm
iteration is higher. An example is the BFGS method which consists in calculating on every step a matrix by which the gradient vector is multiplied to
Gradient_descent
Pairwise-comparison electoral system
methods, such as Ranked Pairs and the Schulze method, use the information contained in the sum matrix to choose a winner. Cells marked '—' in the matrices
Condorcet_method
Matrix operation which flips a matrix over its diagonal
AT is an n × m matrix. A square matrix whose transpose is equal to itself is called a symmetric matrix; that is, A is symmetric if A T = A . {\displaystyle
Transpose
Numerical variational technique
lowest-energy matrix product state wavefunction of a Hamiltonian. It was invented in 1992 by Steven R. White and it is nowadays the most efficient method for 1-dimensional
Density matrix renormalization group
Density_matrix_renormalization_group
Ionization technique
liquid matrix method" that combined 30 nm cobalt particles in glycerol with a 337 nm nitrogen laser for ionization. Using this laser and matrix combination
Matrix-assisted laser desorption/ionization
Matrix-assisted_laser_desorption/ionization
Correspondence between quaternions and 3D rotations
zero or very small. For a stable method of converting an orthogonal matrix to a quaternion, see the Rotation matrix#Quaternion. The above section described
Quaternions and spatial rotation
Quaternions_and_spatial_rotation
Method used in supply chain management
In supply chain management, the Kraljic matrix (or Kraljic model) is a method used to segment the purchases or suppliers of a company by dividing them
Kraljic_matrix
Method for finding largest (or smallest) eigenvalues
Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is a matrix-free method for finding the largest (or smallest) eigenvalues and the corresponding
LOBPCG
Algorithm for linear programming
simplex method) is an algorithm for linear programming. The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin
Simplex_algorithm
Algorithmic runtime requirements for matrix multiplication
developing matrix multiplication algorithms to get improved bounds on ω. All recent algorithms in this line of research use the laser method, a generalization
Computational complexity of matrix multiplication
Computational_complexity_of_matrix_multiplication
invertible and Hermitian matrix, and b is nonzero. The conjugate residual method differs from the closely related conjugate gradient method. It involves more
Conjugate_residual_method
Statistical estimation technique
for the residuals. If this is unknown, estimating the covariance matrix gives the method of feasible generalized least squares (FGLS). However, FGLS provides
Generalized_least_squares
T MATRIX-METHOD
T MATRIX-METHOD
Female
English
French form of Latin Maria, MARIE means "obstinacy, rebelliousness" or "their rebellion."
Male
Hungarian
Hungarian form of Old High German Bernhard, BERNÃT means "bold as a bear."
Female
German
Pet form of German Katarine, KATRIN means "pure."
Male
Hungarian
Czech and Hungarian form of Greek Patrikios, PATRIK means "patrician, of noble descent."
Female
Finnish
Pet form of Finnish Katariina, KATRI means "pure."
Girl/Female
Arabic, Australian, Basque, French, Latin
Lady; Feminine of Martin; Warlike
Female
English
English form of Latin Viatrix, BEATRIX means "voyager (through life)."
Male
Italian
Italian form of Hebrew Mattithyah, MATTIA means "gift of God."
Female
Welsh
Welsh form of Old French Caterine, CATRIN means "pure."
Female
Icelandic
Icelandic form of Latin Margarita, MARGRÉT means "pearl."
Male
French
French and German form of Greek Mattathias, MATHIS means "gift of God."
Female
English
Pet form of English Matilda, MATTIE means "mighty in battle." Compare with masculine Mattie.
Male
English
Pet form of English Martin, MARTIE means "of/like Mars."
Male
Hungarian
Czech and Hungarian form of Latin Donatus, DONÃT means "given (by God)."
Female
Finnish
Finnish form of Greek Margarites, MAARIT means "pearl."
Female
Finnish
Finnish form of Greek Maria, MAARIA means "obstinacy, rebelliousness" or "their rebellion."Â
Male
French
 French form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Male
English
Pet form of English Matthew, MATTIE means "gift of God." Compare with feminine Mattie.
Male
English
 English form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Male
English
Anglicized form of Irish Gaelic MainchÃn, MANNIX means "little monk."
T MATRIX-METHOD
T MATRIX-METHOD
Surname or Lastname
English
English : nickname for a man with curly hair, from Middle English crisp, Old English crisp, cryps (Latin crispus), reinforced in Middle English by an Old French word also from Latin crispus.Americanized spelling of the German cognate Krisp, from Middle High German krisp, krispel ‘curly-haired man’.Americanized form of German Krisp, from a short form the medieval personal name Krispin (see Crispin).
Boy/Male
American, British, English
Charcoal Merchant; Coal Seller
Boy/Male
Tamil
Wisdom, Water Lily
Boy/Male
Tamil
Abimanyu | அபீமாஂநà¯à®¯à¯à®‚
Arjunas son, Heroic, With self respect
Boy/Male
Indian, Sanskrit
Cowherd
Boy/Male
Indian
The reckoner
Girl/Female
Indian, Modern, Punjabi, Sikh
Very Rich; God Gift
Boy/Male
Tamil
Praneeth is the name derived from the Sanskrit word praneetham which means calmness
Girl/Female
Arabic, Australian, German, Latin, Muslim
Queen; Wise Guardian; Form of Regina
Male
Danish
, ornamental bear.
T MATRIX-METHOD
T MATRIX-METHOD
T MATRIX-METHOD
T MATRIX-METHOD
T MATRIX-METHOD
v. t.
See Entail, v. t.
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.
v. t.
See Cob, v. t.
pl.
of Matrix
n.
See Matrix.
v. t.
See Roust, v. t.
v. t.
See Buttweld, v. t.
v. t.
See Kittle, v. t.
v. t.
See Kiddy, v. t.
pl.
of Maori
v. t.
The white fibrous matter forming the matrix from which fungi.
v. t.
See Jam, v. t.
v. t.
See Leach, v. t.
a.
Of or pertaining to the Maoris or to their language.
n.
A mold; a matrix.