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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
Topics referred to by the same term
Dibromomescaline, a psychedelic drug Dibromomethane, a halomethane Difference bound matrix, a data structure used in a field of computer science Dibutyl maleate
DBM
1999 film by the Wachowskis
success of the Wachowskis' 1996 film Bound, Warner Bros. gave the directing duo the go-ahead to make The Matrix. The film's action scenes were influenced
The_Matrix
Algorithmic runtime requirements for matrix multiplication
computer science. As of January 2024[update], the best bound on the asymptotic complexity of a matrix multiplication algorithm is O(n2.371339). However, this
Computational complexity of matrix multiplication
Computational_complexity_of_matrix_multiplication
Topics referred to by the same term
management Zone (convex polytope), in model checking, a type of difference bound matrix Thermal zone, or just zone, in heating, ventilating, and air conditioning
Zone
Square matrix used to represent a graph or network
computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices
Adjacency_matrix
of bounding the differences by applying Azuma's inequality to a Doob martingale. A version of the bounded differences inequality holds in the matrix setting
Matrix_Chernoff_bound
Limit on the parameters of a block code
the Hamming bound is a limit on the parameters of an arbitrary block code: it is also known as the sphere-packing bound or the volume bound from an interpretation
Hamming_bound
American filmmakers
their careers. They made their directing debut with Bound (1996), and achieved fame with The Matrix (1999), a major box-office success for which they won
The_Wachowskis
Mathematics concept
n × n Hadamard matrix has the maximum possible n-dimensional volume among parallelotopes spanned by vectors whose entries are bounded in absolute value
Hadamard_matrix
Array of numbers
In mathematics, a matrix (pl.: matrices) is a rectangular array of numbers or other mathematical objects with elements or entries arranged in rows and
Matrix_(mathematics)
Computer science metric for string similarity
science, the Levenshtein distance is a string metric for measuring the difference between two sequences. The Levenshtein distance between two words is the
Levenshtein_distance
Dimension of the column space of a matrix
rows and columns. A matrix is said to be rank-deficient if it does not have full rank. The rank deficiency of a matrix is the difference between the lesser
Rank_(linear_algebra)
Upper limit on entropy in physics
divergences. In the case of the Bekenstein bound, ultraviolet divergences can be avoided by taking differences between quantities computed in an excited
Bekenstein_bound
Algorithm to multiply matrices
complexity of matrix multiplication) remains unknown. As of September 2025[update], the best bound on the asymptotic complexity of a matrix multiplication
Matrix multiplication algorithm
Matrix_multiplication_algorithm
Property of a mathematical matrix
In mathematics, a symmetric matrix M {\displaystyle M} with real entries is positive-definite if the real number x T M x {\displaystyle \mathbf {x} ^{\mathsf
Definite_matrix
Smallest unit of a chemical element
of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished from each other
Atom
Concepts from linear algebra
-a_{k}=0,} which can 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
Eigenvalues_and_eigenvectors
Space within the inner membrane of the mitochondrion
mitochondrion, the matrix is the space within the inner membrane. It can also be referred as the mitochondrial fluid. The word "matrix" stems from the fact
Mitochondrial_matrix
Discrete fourier transform expressed as a matrix
applied mathematics, a DFT matrix is a square matrix as an expression of a discrete Fourier transform (DFT) as a transformation matrix, which can be applied
DFT_matrix
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 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
Problem in computer science
Such lower bound is called a "separation bound" since it separates between the difference and 0. For example, if the absolute difference is at least
Square-root_sum_problem
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
Method for estimating the unknown parameters in a linear regression model
take the form of requiring that {xiεi} is a martingale difference sequence, with a finite matrix of second moments Qxxε² = E[ εi2xi xiT ]. Suppose it is
Ordinary_least_squares
Lewandowski-Kurowicka-Joe distribution The matrix normal distribution The matrix t-distribution The Matrix Langevin distribution The matrix variate beta distribution The
List of probability distributions
List_of_probability_distributions
Principle in theoretical physics
correspondence. The holographic principle was inspired by the Bekenstein bound of black hole thermodynamics, which conjectures that the maximum entropy
Holographic_principle
Function's sensitivity to argument change
many different directions, and is thus computed from the geometry of the matrix. More generally, condition numbers can be defined for non-linear functions
Condition_number
Result about when a matrix can be diagonalized
result about when a linear operator or matrix can be diagonalized (that is, represented as a diagonal matrix in some basis). This is extremely useful
Spectral_theorem
Method for model fitting in statistics
matrix of the errors are null. The fit of a model to a data point is measured by its residual, r i {\displaystyle r_{i}} , defined as the difference between
Weighted_least_squares
Mathematical function often applied to matrices
subordinate to the matrix norms. For real-valued nonlinear maps there are various possibilities to define operator norms. The least upper bound Lipschitz constant
Logarithmic_norm
Substitution cipher based on linear algebra
7n^{2}} is an upper bound on the key size of the Hill cipher using n × n matrices. This is only an upper bound because not every matrix is invertible and
Hill_cipher
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
Type of tissue that connects muscle to bone
tendon cells (tenocytes). Tendon cells synthesize the tendon's extracellular matrix, which abounds with densely-packed collagen fibers. The collagen fibers
Tendon
Numerical analysis technique
expansion Beam propagation method Finite-difference frequency-domain Finite element method Scattering-matrix method Discrete dipole approximation J. von
Finite-difference time-domain method
Finite-difference_time-domain_method
Mathematical concept
norms provide a way to quantify the "distance" or "difference" between the true vector (or matrix) and its approximation in a multi-dimensional space
Approximation_error
Biological mechanism for routing proteins
ribosomes bound to the endoplasmic reticulum (ER). Candidate explanations at the time postulated a processing difference between free and ER-bound ribosomes
Protein_targeting
Characteristic polynomial whose associated linear system is stable
and difference equations. A linear, time-invariant system (see LTI system theory) is said to be BIBO stable if every bounded input produces bounded output
Stable_polynomial
A {\displaystyle A} is an n × n {\displaystyle n\times n} WCDD L-matrix, we can bound its inverse as follows: ‖ A − 1 ‖ ∞ ≤ ∑ i [ a i i ∏ j = 1 i ( 1 −
Weakly chained diagonally dominant matrix
Weakly_chained_diagonally_dominant_matrix
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
Linear algebra aspects of graph theory
such as its adjacency matrix or Laplacian matrix. The adjacency matrix of a simple undirected graph is a real symmetric matrix and is therefore orthogonally
Spectral_graph_theory
Mathematical concept
form a vector space, whose dimension is the difference between the number of unknowns and the rank of the matrix of the system. The main property of linear
Underdetermined_system
Chemical compound
Its structure is similar to that of the guanosine nucleoside, the only difference being that nucleotides like GTP have phosphates on their ribose sugar
Guanosine_triphosphate
Probability distribution
Cramér–Rao bound, since the Fisher information matrix components for the beta distribution are these logarithmic variances. The Cramér–Rao bound states that
Beta_distribution
Theorem in linear algebra
In matrix theory, the Perron–Frobenius theorem, proved in its first part by Oskar Perron (1907) and extended by Georg Frobenius (1912), asserts that a
Perron–Frobenius_theorem
Generative adversarial network variant
\|W_{i}\|_{s}} of each matrix, we can upper-bound the Lipschitz norm of D {\displaystyle D} . Since for any m × l {\displaystyle m\times l} matrix W {\displaystyle
Wasserstein_GAN
Mathematical condition for convergence
solution. As a consequence, the time step must be less than a certain upper bound, given a fixed spatial increment, in many explicit time-marching computer
Courant–Friedrichs–Lewy condition
Courant–Friedrichs–Lewy_condition
Concept in physics
individual chromophores in a solid matrix. The zero-phonon line is located at a frequency ω’ determined by the intrinsic difference in energy levels between ground
Zero-phonon line and phonon sideband
Zero-phonon_line_and_phonon_sideband
Numerical method for solving physical or engineering problems
The matrix L {\displaystyle L} is usually referred to as the stiffness matrix, while the matrix M {\displaystyle M} is dubbed the mass matrix. In general
Finite_element_method
Parameter estimation technique in statistics, particularly econometrics
rule of thumb, a weighting matrix inches closer to optimality when it turns into an expression closer to the Cramér–Rao bound. One difficulty with implementing
Generalized_method_of_moments
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
Alternating-direction implicit method
Alternating-direction_implicit_method
Set of the elements not in a given subset
relative complement of A with respect to a set B, also termed the set difference of B and A, written B ∖ A , {\displaystyle B\setminus A,} is the set of
Complement_(set_theory)
Form of data structure
many programs, associating a geometrical transformation matrix (see also transformation and matrix) at each group level and concatenating such matrices together
Scene_graph
Function that maps matrices to matrices
In mathematics, every analytic function can be used for defining a matrix function that maps square matrices with complex entries to square matrices of
Analytic_function_of_a_matrix
constraint. Zones and clock constraints are implemented using difference bound matrix. Given a model M {\displaystyle M} , it uses a finite number of
Clock_(model_checking)
Branch of ordinary differential equations
space. A matrix ϕ ( t ) {\displaystyle \phi \,(t)} is called a fundamental matrix solution if the columns form a basis of the solution set. A matrix Φ ( t
Floquet_theory
Type of geometric transformation
a shear matrix or transvection, an elementary matrix that represents the addition of a multiple of one row or column to another. Such a matrix may be derived
Shear_mapping
Fermion that is its own antiparticle
In condensed matter physics, quasiparticle excitations can appear like bound Majorana states. However, instead of a single fundamental particle, they
Majorana_fermion
Equations describing classical electromagnetism
magnetic field B, together with the bound charge and current. See below for a detailed description of the differences between the microscopic equations
Maxwell's_equations
American actor (born 1951)
film series (1995–2024), Cypher in the Wachowskis' sci-fi action film The Matrix (1999), and Teddy in Christopher Nolan's psychological thriller film Memento
Joe_Pantoliano
Type of radioactive decay
ground state has a much smaller matrix element." Takahashi, K.; Boyd, R. N.; Mathews, G. J.; Yokoi, K. (1 October 1987). "Bound-state beta decay of highly
Beta_decay
Quantum particle
are obtained by diagonalizing this matrix. This gives new eigenvectors, which we can call K1, which is the difference of the two states of opposite strangeness
Kaon
Arithmetical operation
associativity, and inclusion of identity (the identity matrix) and inverses. However, matrix multiplication is not commutative, which shows that this
Multiplication
Model of an energy potential in quantum mechanics
\end{cases}}} In any one-dimensional attractive potential there will be a bound state. To find its energy, note that for E < 0, k = i√2m|E|/ħ = iκ is imaginary
Delta_potential
Mapping function that preserves data point locality
paper. Buluç et al. present a sparse matrix data structure that Z-orders its non-zero elements to enable parallel matrix-vector multiplication. Matrices in
Z-order_curve
Basic unit of life forms
cells, which excludes the haploid gametes. Prokaryotes lack a membrane-bound nucleus and have a nucleoid instead. In eukaryotic cells, the nucleus is
Cell_(biology)
Mathematician, programmer
they published in their paper titled "On the p-rank of the design matrix of a difference set". One of MacWilliams' significant achievements was her encyclopedic
Jessie_MacWilliams
Equation used in quantum scattering problems
Big Bang. In the 1960s, the S-matrix paradigm was elevated by many physicists to a fundamental law of nature. In S-matrix theory, it was stated that any
Lippmann–Schwinger_equation
Discrete Fourier transform algorithm
practical. An FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse (mostly zero) factors. As a result, it manages
Fast_Fourier_transform
True when either but not both inputs are true
) ∧ ¬ ( p ∧ q ) {\displaystyle {\begin{matrix}p\nleftrightarrow q&=&(p\vee q)\land \neg (p\land q)\end{matrix}}} The exclusive disjunction p ↮ q {\displaystyle
Exclusive_or
Method of data analysis
a spike. The eigenvectors of the difference between the spike-triggered covariance matrix and the covariance matrix of the prior stimulus ensemble (the
Principal_component_analysis
Copy of a directed graph with redundant edges removed
exact algorithms for matrix multiplication, as of 2023, take time O(n2.371552), and this gives the fastest known worst-case time bound for transitive reduction
Transitive_reduction
Ionization technique
spectrometry, matrix-assisted laser desorption/ionization (MALDI) is an ionization technique that uses a laser energy-absorbing matrix to create ions
Matrix-assisted laser desorption/ionization
Matrix-assisted_laser_desorption/ionization
Formal language generated by context-free grammar
Boolean matrix multiplication, thus inheriting its complexity upper bound of O(n2.3728596). Conversely, Lillian Lee has shown O(n3−ε) Boolean matrix multiplication
Context-free_language
The Fannes–Audenaert inequality is a mathematical bound on the difference between the von Neumann entropies of two density matrices as a function of their
Fannes–Audenaert_inequality
Expression for sums of powers
(column) are bound by a given matrix order m {\displaystyle m} . To generalize up to p = 4 {\displaystyle p=4} , apply the above formula for matrix order m
Faulhaber's_formula
Conjecture on zeros of the zeta function
corresponding random-matrix ensembles. For the Riemann zeta function, the relevant ensemble is that of the unitary group. Random matrix theory has also led
Riemann_hypothesis
Family of linear transformations
ζ is small, and Bx is simply the boost matrix in the x direction. The derivative of the matrix is the matrix of derivatives (of the entries, with respect
Lorentz_transformation
Numerical eigenvalue calculation
eigenvalues and eigenvectors of an n × n {\displaystyle n\times n} Hermitian matrix, where m {\displaystyle m} is often but not necessarily much smaller than
Lanczos_algorithm
Gradient of electrochemical potential, usually for an ion that can move across a membrane
parts: The chemical gradient, or difference in solute concentration across a membrane. The electrical gradient, or difference in charge across a membrane.
Electrochemical_gradient
Analog of the continuous Laplace operator
vertices), the discrete Laplace operator is more commonly called the Laplacian matrix. The discrete Laplace operator occurs in physics problems such as the Ising
Discrete_Laplace_operator
Recursive algorithm for matrix multiplication
named after Volker Strassen, is an algorithm for matrix multiplication. It is faster than the standard matrix multiplication algorithm for large matrices,
Strassen_algorithm
Principle in mathematical optimization
{\displaystyle \sup } denotes the supremum (least upper bound). The duality gap is the difference between the values of any primal solutions and any dual
Duality_(optimization)
Statistical measure of the magnitude of a phenomenon
between two variables, the regression coefficient in a regression, the mean difference, and the risk of a particular event (such as a heart attack). Effect sizes
Effect_size
Efficient reconstruction of quantum states based on measurements
{\displaystyle {\langle }P_{s}\rangle =1} holds. This way, we can lower bound the difference knowing only ϱ P I . {\displaystyle \varrho _{\rm {PI}}.} There are
Permutationally invariant quantum state tomography
Permutationally_invariant_quantum_state_tomography
Deep learning generative model to encode data representation
}z)|} where ∂ ϵ z {\displaystyle \partial _{\epsilon }z} is the Jacobian matrix of z {\displaystyle z} with respect to ϵ {\displaystyle \epsilon } . Since
Variational_autoencoder
Problem in linear algebra
of the permanent of a matrix is a problem that is thought to be more difficult than the computation of the determinant of a matrix despite the apparent
Computing_the_permanent
Tissue surrounding chondrocytes in cartilage
components. The territorial matrix is one of three major regions of the extracellular matrix; it is surrounded by the pericellular matrix and the interterritorial
Territorial_matrix
Liquid found in cells
The cytosol, also known as cytoplasmic matrix or groundplasm, is one of the liquids found inside cells (intracellular fluid (ICF)). It is separated into
Cytosol
Line formed by the real numbers
can be represented in matrix form as the n-by-n identity matrix, the metric on the real line is simply the 1-by-1 identity matrix, i.e. 1. If p ∈ R and
Number_line
Number of disease cases in a given population at a specific time
characteristic curve), a condition with a relatively low prevalence or base-rate is bound to yield high false positive rates, which exceed false negative rates; in
Prevalence
Enzyme
inactivate the MMP. MMPs are associated with the cell surface or bound to the extracellular matrix which prevents them from diffusing away and keeps the MMP
Metalloprotease_inhibitor
NP-hard problem in combinatorial optimization
Salesman Problem - Branch and Bound on YouTube. How to cut unfruitful branches using reduced rows and columns as in Hungarian matrix algorithm Applegate, David;
Travelling_salesman_problem
Volume rendering technique
ellipsoid, which can be mathematically decomposed into a scaling matrix and a rotation matrix. The gradients for all parameters are derived explicitly to overcome
Gaussian_splatting
Polynomial interpolation using derivative values
interpolation polynomial as unknown variables and a confluent Vandermonde matrix as its matrix. The general methods of linear algebra, and specific methods for
Hermite_interpolation
science, denotes the (unknown) greatest lower bound for the exponent of the computational complexity of matrix multiplication. 4. Written as a function of
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Geometric object that has length and direction
n3 as the n basis, the matrix containing all the cjk is known as the "transformation matrix from e to n", or the "rotation matrix from e to n" (because
Euclidean_vector
Theory about lossy data compression
mostly limited to the JPEG and MPEG weighting (quantization, normalization) matrix. Distortion functions measure the cost of representing a symbol x {\displaystyle
Rate–distortion_theory
Fundamental theorem in probability theory and statistics
linear function of a matrix M is a linear combination of its elements (with given coefficients), M ↦ tr(AM) where A is the matrix of the coefficients;
Central_limit_theorem
Statistical test
of the matrix, while differences between the outcomes for each treatment are represented on the right-hand side. After obtaining the difference scores
Mauchly's_sphericity_test
DIFFERENCE BOUND-MATRIX
DIFFERENCE BOUND-MATRIX
Boy/Male
Indian, Marathi
Raindrops
Surname or Lastname
English
English : variant of Bond.
Girl/Female
Assamese, Hindu, Indian, Marathi
Bound
Surname or Lastname
English (found mainly in Wales)
English (found mainly in Wales) : variant of Glasscock 2.
Boy/Male
English
Tied to the land.
Surname or Lastname
English
English : from Middle English p(o)und ‘enclosure (especially for confining animals)’; a topographic name for someone who lived near an enclosure in which animals were kept, or a metonymic occupational name for an official responsible for rounding up stray animals and placing them in a pound.Probably a translation of German Pfund or the North German cognate Pund.
Girl/Female
Biblical
Bound, limit.
Surname or Lastname
English
English : variant of Bond
Girl/Female
Hindu, Indian, Tamil
Drop
Surname or Lastname
English
English : status name for a peasant farmer or husbandman, Middle English bonde (Old English bonda, bunda, reinforced by Old Norse bóndi). The Old Norse word was also in use as a personal name, and this has given rise to other English and Scandinavian surnames alongside those originating as status names. The status of the peasant farmer fluctuated considerably during the Middle Ages; moreover, the underlying Germanic word is of disputed origin and meaning. Among Germanic peoples who settled to an agricultural life, the term came to signify a farmer holding lands from, and bound by loyalty to, a lord; from this developed the sense of a free landholder as opposed to a serf. In England after the Norman Conquest the word sank in status and became associated with the notion of bound servitude.Swedish : variant of Bonde.
Surname or Lastname
English (chiefly West Midlands)
English (chiefly West Midlands) : nickname for a plump person, from Middle English, Old French rond, rund ‘fat’, ‘round’ (Latin rotundus).
Girl/Female
Arabic, Muslim
Distinction; Difference; Manner
Girl/Female
Tamil
Bandini | பநà¯à®¤à¯€à®¨à¯€Â
A bond, One who glues together, Is bound, Preserve
Bandini | பநà¯à®¤à¯€à®¨à¯€Â
Surname or Lastname
English
English : presumably a variant of Mount.
Girl/Female
Indian
A bond, One who glues together, Is bound, Preserve
Surname or Lastname
English
English : patronymic from Bond.
Boy/Male
American, Australian, British, Christian, English, German, Indian
Tied to the Land; Tiller of the Soil; Farmer
Male
English
Farmer
Boy/Male
Hindu, Indian
Difference
Girl/Female
Australian, Danish, Finnish, German, Hebrew, Japanese, Netherlands, Scandinavian
Blind; Bound
DIFFERENCE BOUND-MATRIX
DIFFERENCE BOUND-MATRIX
Boy/Male
Italian
brilliant raven; Fiery torch; beacon.
Female
Danish
, of Apollo.
Boy/Male
American, British, English
Little; Son of Paul; Surname
Boy/Male
Muslim
Complete. Perfect.
Boy/Male
Danish, German, Swedish
High Son; Enclosure
Boy/Male
Hindu, Indian, Malayalam, Marathi, Sanskrit
An Epithet for Yama
Girl/Female
Hindu
Refreshing
Boy/Male
Tamil
Praachik | பà¯à®°à®¾à®šà®¿à®•
Long-legged
Girl/Female
British, English
Polite
Boy/Male
Indian, Sikh
Officer
DIFFERENCE BOUND-MATRIX
DIFFERENCE BOUND-MATRIX
DIFFERENCE BOUND-MATRIX
DIFFERENCE BOUND-MATRIX
DIFFERENCE BOUND-MATRIX
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?
a.
Uttered or emitted with a full tone; as, a round voice; a round note.
n.
Rebound; as, the bound of a ball.
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.
v. t.
To cause to differ; to make different; to mark as different; to distinguish.
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.
Anything round, as a circle, a globe, a ring. "The golden round" [the crown].
superl.
Whole; unbroken; unharmed; free from flaw, defect, or decay; perfect of the kind; as, sound timber; sound fruit; a sound tooth; a sound ship.
imp. & p. p.
of Difference
superl.
Founded in truth or right; supported by justice; not to be overthrown on refuted; not fallacious; as, sound argument or reasoning; a sound objection; sound doctrine; sound principles.
n.
The state of being bound; imprisonment; captivity, restraint.
p. p. & a.
Inclosed in a binding or cover; as, a bound volume.
v. t.
To make to bound or leap; as, to bound a horse.
n.
That which goes round a whole circle or company; as, a round of applause.
v. t.
To cause to rebound; to throw so that it will rebound; as, to bound a ball on the floor.
v. t.
To order, direct, indicate, or proclain by a sound, or sounds; to give a signal for by a certain sound; as, to sound a retreat; to sound a parley.
pl.
of Pound
p. p. & a.
Resolved; as, I am bound to do it.
v. t.
To name the boundaries of; as, to bound France.
p. p. & a.
Constrained or compelled; destined; certain; -- followed by the infinitive; as, he is bound to succeed; he is bound to fail.