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Relation of a matrix of variables between two points in time
A matrix difference equation is a difference equation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related
Matrix_difference_equation
Pattern defining an infinite sequence of numbers
and "difference equation" can be used interchangeably. See Rational difference equation, Linear constant-coefficient difference equation and Matrix difference
Recurrence_relation
Functional equation Functional equation (L-function) Constitutive equation Laws of science Defining equation (physical chemistry) List of equations in classical
List_of_equations
Matrix whose entries are the coefficients of a linear equation
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 systems
Coefficient_matrix
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)
Type of mathematical equation
derivatives of various orders. A matrix differential equation contains more than one function stacked into vector form with a matrix relating the functions to
Matrix_differential_equation
Matrix used to describe the transitions of a Markov chain
{1} \,.} Density matrix Markov kernel, the equivalent of a stochastic matrix over a continuous state space Matrix difference equation Models of DNA evolution
Stochastic_matrix
Mathematical relation defining a sequence
coefficients (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates
Linear recurrence with constant coefficients
Linear_recurrence_with_constant_coefficients
Class of numerical techniques
finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences.
Finite_difference_method
Polynomial whose roots are the eigenvalues of a matrix
I} is the identity matrix, and v ≠ 0 {\displaystyle \mathbf {v} \neq \mathbf {0} } (although the zero vector satisfies this equation for every λ , {\displaystyle
Characteristic_polynomial
Formulation of quantum mechanics
frequency. To determine the matrix elements, Heisenberg required that the classical equations of motion be obeyed as matrix equations, d X d t = P , d P d
Matrix_mechanics
Several equations of degree 1 to be solved simultaneously
The vector equation is equivalent to a matrix equation of the form A x = b {\displaystyle A\mathbf {x} =\mathbf {b} } where A is an m×n matrix, x is a column
System_of_linear_equations
Discrete analog of a derivative
[f](x)=f(x+1)-f(x).} A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves
Finite_difference
Limiting set in dynamical systems
entire number line is the basin of attraction. Likewise, a linear matrix difference equation in a dynamic vector X {\displaystyle X} , of the homogeneous form
Attractor
Equation used in quantum scattering problems
The Lippmann–Schwinger equation (named after Bernard Lippmann and Julian Schwinger) is one of the most used equations to describe particle collisions –
Lippmann–Schwinger_equation
A rational difference equation is a nonlinear difference equation of the form x n + 1 = α + ∑ i = 0 k β i x n − i A + ∑ i = 0 k B i x n − i , {\displaystyle
Rational_difference_equation
Representation of a matrix as a sum
differential equations) depend upon the direct solution of matrix equations involving matrices more general than tridiagonal matrices. These matrix equations can
Matrix_splitting
Coefficient used in numerical approximation
the number of stencil points, the finite difference coefficients can be obtained by solving the linear equations ( s 1 0 ⋯ s N 0 ⋮ ⋱ ⋮ s 1 N − 1 ⋯ s N N
Finite_difference_coefficient
Age-structured model of population growth
polynomial of the matrix is given by the Euler–Lotka equation. The Leslie model is very similar to a discrete-time Markov chain. The main difference is that in
Leslie_matrix
Partial differential equation describing the evolution of temperature in a region
specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier
Heat_equation
Mathematical tool in quantum physics
In quantum mechanics, a density matrix (or density operator) is a matrix used in calculating the probabilities of the outcomes of measurements performed
Density_matrix
Concepts from linear algebra
be found by stacking into matrix form a set of equations consisting of the above difference equation and the k – 1 equations xt–1 = xt–1, ..., xt–k+1 =
Eigenvalues_and_eigenvectors
2005 mathematics textbook
roots of characteristic polynomials, the Leslie matrix in population dynamics, matrix difference equations and Markov chains, recurrences in modular arithmetic
Difference Equations: From Rabbits to Chaos
Difference_Equations:_From_Rabbits_to_Chaos
Differential equation that is linear with respect to the unknown function
In mathematics, a linear differential equation is a differential equation that is linear in the unknown function and its derivatives, so it can be written
Linear_differential_equation
Relativistic quantum mechanical wave equation
significantly across dimensions. Other differences include the absence of a chirality matrix in odd dimensions. The equation can also be generalized from flat
Dirac_equation
Mathematical description of fluid movements
the endothelial cells. This fibre matrix endocapillary layer is called the endothelial glycocalyx. The Starling equation describes that relationship in mathematical
Starling_equation
Nonlinear equation which arises on linear optimal control problems
invariant solutions of the matrix valued Riccati difference equation (which is the analogue of the Riccati differential equation in the context of discrete
Algebraic_Riccati_equation
Quantum consistency equation
scattering matrix and if it satisfies the Yang–Baxter equation then the system is integrable. In quantum integrable models, the Yang–Baxter equation ensures
Yang–Baxter_equation
Matrix operation generalizing exponentiation of scalar numbers
of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding
Matrix_exponential
Type of differential equation
differential equations List of dynamical systems and differential equations topics Matrix differential equation Numerical partial differential equations Partial
Partial_differential_equation
Parameter in differential equations and dynamical systems
conditions is referred to as an initial value problem. A linear matrix difference equation of the homogeneous (having no constant term) form X t + 1 = A
Initial_condition
Set of quasilinear hyperbolic equations governing adiabatic and inviscid flow
In fluid dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard
Euler equations (fluid dynamics)
Euler_equations_(fluid_dynamics)
Method for estimating the unknown parameters in a linear regression model
p} columns of the matrix X {\displaystyle \mathbf {X} } are linearly independent, given by solving the so-called normal equations: ( X T X ) β ^ = X
Ordinary_least_squares
Finite difference method for numerically solving parabolic differential equations
Crank–Nicolson method is a finite difference method used for numerically solving the heat equation and similar partial differential equations. It is a second-order
Crank–Nicolson_method
Matrix formed by appending columns of two other matrices
solutions to a system of k {\displaystyle k} linear equations depends only on the rank of the matrix of coefficients A {\displaystyle A} representing the
Augmented_matrix
Dynamical system
prevalence relative to others. Another key difference from the quasispecies model is that the replicator equation does not include mechanisms for mutation
Replicator_equation
Mandelbrot set Recurrence relation Matrix difference equation Rational difference equation Examples of differential equations Autonomous system (mathematics)
List of dynamical systems and differential equations topics
List_of_dynamical_systems_and_differential_equations_topics
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
Polynomial equation of degree 4
mathematics, a quartic equation is one which can be expressed as a quartic function equaling zero. The general form of a quartic equation is a x 4 + b x 3 +
Quartic_equation
Statistical model to calculate the value of multiple quantities as they change over time
differenced d times and one has a VAR in difference. One can stack the vectors in order to write a VAR(p) as a stochastic matrix difference equation,
Vector_autoregression
Differential equation exhibiting high rate of dissipation
(discretized) Poisson equation − Δ u = f {\displaystyle -\Delta u=f} . Here, the Jacobi method (which attempts to avoid matrix algebra) is equivalent
Stiff_equation
Theorem in numerical analysis
finite difference methods for the numerical solution of linear partial differential equations. It states that for a linear consistent finite difference method
Lax_equivalence_theorem
Numerical method for solving physical or engineering problems
method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas
Finite_element_method
Numerical analysis technique
modeling computational electrodynamics. Finite difference schemes for time-dependent partial differential equations (PDEs) have been employed for many years
Finite-difference time-domain method
Finite-difference_time-domain_method
Antagonist in The Matrix (film series)
negative, a result of the Matrix's equation trying to balance itself. She tells Neo that Smith will destroy both the Matrix and the real world unless
Agent_Smith
Dimension of the column space of a matrix
the system of linear equations and linear transformation encoded by A. There are multiple equivalent definitions of rank. A matrix's rank is one of its
Rank_(linear_algebra)
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
Equations describing classical electromagnetism
Maxwell's equations are a set of coupled partial differential equations that describe how electric and magnetic fields are generated by electric charges
Maxwell's_equations
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
Branch of physics
methods involve: time-stepping through the equations over the whole domain for each time instant; banded matrix inversion to calculate the weights of basis
Computational electromagnetics
Computational_electromagnetics
Vectors mapped to 0 by a linear map
A\mathbf {x} =\mathbf {0} \right\}.} The matrix equation is equivalent to a homogeneous system of linear equations: A x = 0 ⇔ a 11 x 1 + a 12 x 2 + ⋯ + a
Kernel_(linear_algebra)
Matrix representation of a graph
the negative continuous Laplacian obtained by the finite difference method. The Laplacian matrix relates to many functional graph properties. Kirchhoff's
Laplacian_matrix
Matrix with non-zero elements only in a diagonal band
differential equation on a square domain (using central differences) will yield a matrix with a bandwidth equal to the square root of the matrix dimension
Band_matrix
Representation of a type of random process
the form of a stochastic difference equation (or recurrence relation) which should not be confused with a differential equation. Together with the moving-average
Autoregressive_model
Matrix of geometric progressions
Exploiting the structure of the Vandermonde matrix, one can use Newton's divided differences method) to solve the equation in O(n2) time, which also gives the
Vandermonde_matrix
Branch of ordinary differential equations
the linear differential equation form a vector space. A matrix ϕ ( t ) {\displaystyle \phi \,(t)} is called a fundamental matrix solution if the columns
Floquet_theory
Mathematical model of the time dependence of a point in space
system has the form of a matrix difference equation: x n + 1 = A x n + b , {\displaystyle x_{n+1}=Ax_{n}+b,} with A a matrix and b a vector. As in the
Dynamical_system
Differential equation containing derivatives with respect to only one variable
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other
Ordinary differential equation
Ordinary_differential_equation
Polynomial equation of degree 3
In algebra, a cubic equation in one variable is an equation of the form a x 3 + b x 2 + c x + d = 0 {\displaystyle ax^{3}+bx^{2}+cx+d=0} in which a is
Cubic_equation
Numerical solution method of computational electromagnetics
sometimes in acoustics, based on finite-difference approximations of the derivative operators in the differential equation being solved. While "FDFD" is a generic
Finite-difference frequency-domain method
Finite-difference_frequency-domain_method
Methods used to find numerical solutions of ordinary differential equations
ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is
Numerical methods for ordinary differential equations
Numerical_methods_for_ordinary_differential_equations
Mathematical method used in optics and acoustics
infinite number of reflections. The transfer-matrix method is based on the fact that, according to Maxwell's equations, there are simple continuity conditions
Transfer-matrix method (optics)
Transfer-matrix_method_(optics)
System of equations in mathematics
differential-algebraic system of equations (DAE) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to
Differential-algebraic system of equations
Differential-algebraic_system_of_equations
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
Class of second-order linear partial differential equations
A parabolic partial differential equation is a type of partial differential equation (PDE). Parabolic PDEs are used to describe a wide variety of time-dependent
Parabolic partial differential equation
Parabolic_partial_differential_equation
Determinant of the matrix of first derivatives of a set of functions
-st derivative, thus forming a square matrix. When the functions are solutions of a linear differential equation, the Wrońskian can be found explicitly
Wronskian
Scientific journal
Clarivate. Retrieved October 17, 2025. "Journal of Difference Equations and Applications". MIAR: Information Matrix for the Analysis of Journals. University of
Journal of Difference Equations and Applications
Journal_of_Difference_Equations_and_Applications
Equation that describes density changes of a material that is diffusing in a medium
case of anisotropic diffusion, D is a symmetric positive definite matrix, and the equation is written (for three dimensional diffusion) as: ∂ ϕ ( r , t )
Diffusion_equation
Assumption that motions of nuclei and electrons can be separated
the calculation of the nuclear Schrödinger equation. The BO approximation recognizes the large difference between the electron mass and the masses of
Born–Oppenheimer approximation
Born–Oppenheimer_approximation
branch of fundamental physics, the matrix representations of the Maxwell's equations are a formulation of Maxwell's equations using matrices, complex numbers
Matrix representation of Maxwell's equations
Matrix_representation_of_Maxwell's_equations
More equations than unknowns (mathematics)
the first one. Any system of linear equations can be written as a matrix equation. The previous system of equations (in Diagram #1) can be written as follows:
Overdetermined_system
Curve from a cone intersecting a plane
of the matrix ( A B / 2 B / 2 C ) {\displaystyle \left({\begin{matrix}A&B/2\\B/2&C\end{matrix}}\right)} — that is, the solutions of the equation λ 2 −
Conic_section
Kreiss to analyze the stability of finite difference methods for partial difference equations. Given a matrix A, the Kreiss constant 𝒦(A) (with respect
Kreiss_matrix_theorem
Matrix representing the effect of scattering on a physical system
scattering matrix – a unitary matrix of coefficients connecting "the asymptotic behaviour of an arbitrary particular solution [of the integral equations] with
S-matrix
Relativistic wave equation in quantum mechanics
publish it. He lost confidence in the equation after he did not manage to use it to establish the equivalence between matrix mechanics and wave mechanics, like
Klein–Gordon_equation
In model checking, a field of computer science, a difference bound matrix (DBM) is a data structure used to represent some convex polytopes called zones
Difference_bound_matrix
Fictional character
also known as The One) is a fictional character and the protagonist of The Matrix franchise, created by the Wachowskis. He was portrayed as a cybercriminal
Neo_(The_Matrix)
Finite difference equation
In mathematics, the discrete Poisson equation is the finite difference analog of the Poisson equation. In it, the discrete Laplace operator takes the place
Discrete_Poisson_equation
Representation of a matrix as a product
efficient matrix algorithms. For example, when solving a system of linear equations A x = b {\displaystyle A\mathbf {x} =\mathbf {b} } , the matrix A can
Matrix_decomposition
Analog of the continuous Laplace operator
{d\phi }{dt}}+kL\phi =0.} Notice that this equation takes the same form as the heat equation, where the matrix −L is replacing the Laplacian operator ∇
Discrete_Laplace_operator
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
Method for solving continuous operator problems (such as differential equations)
\quad f_{i}=f(e_{i}).} Due to the definition of the matrix entries, the matrix of the Galerkin equation is symmetric if and only if the bilinear form a (
Galerkin_method
Field of mathematics
statistics. Matrix methods are particularly used in finite difference methods, finite element methods, and the modeling of differential equations. Noting
Numerical_linear_algebra
Mathematical condition for convergence
partial differential operator has been approximated by a finite difference equation, which is then solved by numerical linear algebra methods. This quantity
Courant–Friedrichs–Lewy condition
Courant–Friedrichs–Lewy_condition
Mathematical concept
linear equations (underdetermined or otherwise) is inconsistent if the rank of the augmented matrix is greater than the rank of the coefficient matrix. If
Underdetermined_system
Concept in differential equation mathematics
the spectral radius of the update matrix A ( Δ t ) {\displaystyle A(\Delta t)} . For the linear structural equation M u ¨ + C u ˙ + K u = f ext {\displaystyle
Newmark-beta_method
Ability of a body to store an electrical charge
equation. The definition of capacitance, 1 C ≡ Δ V Δ Q , {\displaystyle {1 \over C}\equiv {\Delta V \over \Delta Q},} with the potential difference Δ
Capacitance
Iterative method used to solve a linear system of equations
linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel. Though it can be applied to any matrix with
Gauss–Seidel_method
Relations between flows and forces, or gradients, in thermodynamic systems
(deformation produced by a voltage difference) coefficients are equal. For many kinetic systems, like the Boltzmann equation or chemical kinetics, the Onsager
Onsager_reciprocal_relations
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
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
Scattering-matrix_method
Iterative method for solving the Sylvester matrix equations
iterative method used to solve Sylvester matrix equations. It is a popular method for solving the large matrix equations that arise in systems theory and control
Alternating-direction implicit method
Alternating-direction_implicit_method
analysis: Sparse matrix Band matrix Bidiagonal matrix Tridiagonal matrix Pentadiagonal matrix Skyline matrix Circulant matrix Triangular matrix Diagonally dominant
List of numerical analysis topics
List_of_numerical_analysis_topics
Form of causal modeling that fit networks of constructs to data
Structural equation modeling (SEM) is a diverse set of methods used by scientists for both observational and experimental research. SEM is used mostly
Structural_equation_modeling
Type of mathematical expression
identity matrix. A matrix polynomial equation is an equality between two matrix polynomials, which holds for the specific matrices in question. A matrix polynomial
Polynomial
Polynomial function of degree 4
polynomial of the matrix. The characteristic equation of a fourth-order linear difference equation or differential equation is a quartic equation. An example
Quartic_function
Property of a mathematical matrix
{\displaystyle N} a symmetric and positive definite matrix. Write the generalized eigenvalue equation as ( M − λ N ) x = 0 {\displaystyle \left(M-\lambda
Definite_matrix
1016/0021-9991(92)90324-R. LeVeque, R.J. (2007). "Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems"
Compact_finite_difference
Numerical method in computational electromagnetics
functions were also introduced to accelerate computation and reduce the matrix equation. The testing and basis functions are often chosen to be the same; this
Method of moments (electromagnetics)
Method_of_moments_(electromagnetics)
Description of the time-evolution of plasma
In plasma physics, the Vlasov equation is a differential equation describing the time evolution of the distribution function of a collisionless plasma
Vlasov_equation
MATRIX DIFFERENCE-EQUATION
MATRIX DIFFERENCE-EQUATION
Female
Finnish
Pet form of Finnish Katariina, KATRI means "pure."
Female
Finnish
Finnish form of Greek Maria, MAARIA means "obstinacy, rebelliousness" or "their rebellion."Â
Girl/Female
Maori
The Maori form of April.
Male
English
 English form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Male
French
 French form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Male
French
French and German form of Greek Mattathias, MATHIS means "gift of God."
Girl/Female
Arabic, Australian, Basque, French, Latin
Lady; Feminine of Martin; Warlike
Female
English
Pet form of English Matilda, MATTIE means "mighty in battle." Compare with masculine Mattie.
Male
English
Anglicized form of Irish Gaelic MainchÃn, MANNIX means "little monk."
Male
English
Pet form of English Matthew, MATTIE means "gift of God." Compare with feminine Mattie.
Male
Italian
Italian form of Hebrew Mattithyah, MATTIA means "gift of God."
Female
English
English form of Latin Viatrix, BEATRIX means "voyager (through life)."
Male
English
Pet form of English Martin, MARTIE means "of/like Mars."
Female
Finnish
Finnish form of Greek Margarites, MAARIT means "pearl."
Female
German
Pet form of German Katarine, KATRIN means "pure."
Female
English
French form of Latin Maria, MARIE means "obstinacy, rebelliousness" or "their rebellion."
Surname or Lastname
English (of Welsh origin)
English (of Welsh origin) : variant of Maddox.
Male
Hungarian
Czech and Hungarian form of Greek Patrikios, PATRIK means "patrician, of noble descent."
Boy/Male
Hindu, Indian
Difference
Female
Welsh
Welsh form of Old French Caterine, CATRIN means "pure."
MATRIX DIFFERENCE-EQUATION
MATRIX DIFFERENCE-EQUATION
Boy/Male
Hindu, Indian
Light; Interest; One who Gives Happiness
Boy/Male
Muslim/Islamic
Matyr of Islam
Girl/Female
Muslim/Islamic
Face like a moon beautiful
Surname or Lastname
English
English : patronymic from the Middle English personal name Clac (see Clack).
Girl/Female
Arabic, Muslim
Blessed; Fortunate; Lucky
Girl/Female
Australian, French
Of the Nobility; Noble
Girl/Female
Sikh
One who becomes the embodiment of naam
Biblical
a young man; a virgin; a secret
Boy/Male
Tamil
Cloud
Boy/Male
Irish
Renowned; noble.
MATRIX DIFFERENCE-EQUATION
MATRIX DIFFERENCE-EQUATION
MATRIX DIFFERENCE-EQUATION
MATRIX DIFFERENCE-EQUATION
MATRIX DIFFERENCE-EQUATION
a.
Of or pertaining to the Maoris or to their language.
a.
Of various or contrary nature, form, or quality; partially or totally unlike; dissimilar; as, different kinds of food or drink; different states of health; different shapes; different degrees of excellence.
n.
The five simple colors, black, white, blue, red, and yellow, of which all the rest are composed.
n.
A mold; a matrix.
n.
Absence of anxiety or interest in respect to what is presented to the mind; unconcernedness; as, entire indifference to all that occurs.
n.
The act of differing; the state or measure of being different or unlike; distinction; dissimilarity; unlikeness; variation; as, a difference of quality in paper; a difference in degrees of heat, or of light; what is the difference between the innocent and the guilty?
n.
Difference of quality or property in different directions.
n.
See Matrix.
v. t.
To cause to differ; to make different; to mark as different; to distinguish.
pl.
of Maori
pl.
of Matrix
imp. & p. p.
of Difference
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.
The quality or state of being indifferent, or not making a difference; want of sufficient importance to constitute a difference; absence of weight; insignificance.
n.
A rectangular arrangement of symbols in rows and columns. The symbols may express quantities or operations.
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.
n.
The earthy or stony substance in which metallic ores or crystallized minerals are found; the gangue.
n.
The lifeless portion of tissue, either animal or vegetable, situated between the cells; the intercellular substance.
n.
Estimation of difference; regard to differences or distinguishing circumstance.