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Topics referred to by the same term
Transition matrix may refer to: Change-of-basis matrix, associated with a change of basis for a vector space. Stochastic matrix, a square matrix used to
Transition_matrix
Matrix used to describe the transitions of a Markov chain
It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix. The stochastic matrix was first developed by Andrey Markov
Stochastic_matrix
Describes state evolution of a linear system
In control theory and dynamical systems theory, the state-transition matrix is a matrix function that describes how the state of a linear system changes
State-transition_matrix
Matrix describing continuous-time Markov chains
In probability theory, a transition-rate matrix (also known as a Q-matrix, intensity matrix, or infinitesimal generator matrix) is an array of numbers
Transition-rate_matrix
Random process independent of past history
process is characterized by a state space, a transition matrix describing the probabilities of particular transitions, and an initial state (or initial distribution)
Markov_chain
Matrices similar to diagonal matrices
square matrix A is called diagonalizable or non-defective if it is similar to a diagonal matrix. That is, if there exists an invertible matrix P and a
Diagonalizable_matrix
Algorithm in mathematics
which leads to the definition of the time-independent stochastic transition matrix A={aij}=P(Xt=j∣Xt−1=i). The initial state distribution (i.e. when
Baum–Welch_algorithm
Predecessor to modern quantum mechanics (1900–1925)
collaboration with Werner Heisenberg to a semiclassical matrix-like description of atomic transition probabilities. Heisenberg went on to reformulate all
Old_quantum_theory
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
Markov chain in which all states can be absorbing
absorbing is called transient. Let an absorbing Markov chain with transition matrix P have t transient states and r absorbing states. The rows of P represent
Absorbing_Markov_chain
includes the probability of a given transition into the transition function, turning it into a transition matrix. Thus, the probabilistic automaton also
Probabilistic_automaton
Matrix representation of a graph
theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian, is a matrix representation of a
Laplacian_matrix
Array of numbers
[19−13205−6] denotes a matrix with two rows and three columns. This is often referred to as a "two-by-three matrix", a 2 × 3 matrix, or a matrix of dimension 2 × 3
Matrix_(mathematics)
1999 film by the Wachowskis
The Matrix is a 1999 science fiction–action film written and directed by the Wachowskis. The first installment in the Matrix film series, it stars Keanu
The_Matrix
Examples of the probabilistic construct
weather on the preceding day, can be represented by a transition matrix: P=[0.90.10.50.5] The matrix P represents the weather model in which a sunny day
Examples_of_Markov_chains
American media franchise
The Matrix is an American cyberpunk media franchise consisting of four feature films, beginning with The Matrix (1999) and continuing with three sequels
The_Matrix_(franchise)
Probability concept
E2∼Exp(18). When a transition is to be made, the process moves according to the jump chain, a discrete-time Markov chain with stochastic matrix: [012121302356160]
Continuous-time_Markov_chain
Dynamic system property
𝐱˙(t)=A(t)𝐱(t)+B(t)𝐮(t)𝐲(t)=C(t)𝐱(t)+D(t)𝐮(t). The state-transition matrix ϕ is also smooth. Introduce the n × m matrix-valued function M0(t) = ϕ(t0, t)B(t) and define
Controllability
Concept in probability theory
in the general theory of Markov processes plays the role that the transition matrix does in the theory of Markov processes with a finite state space.
Markov_kernel
2003 film by the Wachowskis
consciousness is trapped in a subway station named Mobil Ave, a transition zone between the Matrix and the machine world. He meets a "family" of programs, including
The_Matrix_Revolutions
Type of square matrix
probability and combinatorics, a doubly stochastic matrix (also called bistochastic matrix) is a square matrix X = ( x i j ) {\displaystyle X=(x_{ij})} of nonnegative
Doubly_stochastic_matrix
Coordinate change in linear algebra
"new" (other) bases. A is the change-of-basis matrix (also called transition matrix), which is the matrix whose columns are the coordinates of the "new"
Change_of_basis
Property of measure-preserving dynamical systems
by a matrix P ∈ [ 0 , 1 ] S × S {\displaystyle P\in [0,1]^{S\times S}} , where P ( s 1 , s 2 ) {\displaystyle P(s_{1},s_{2})} is the transition probability
Ergodicity
Periodic set of points
{Z} ^{n}} , meaning M ′ = A M {\displaystyle M'=AM} for an integer transition matrix A ∈ G L n ( Z ) {\displaystyle A\in \mathrm {GL} _{n}(\mathbb {Z}
Lattice_(group)
Equation from probability theory
corollary, it follows that to calculate the transition matrix of jump t, it is sufficient to raise the transition matrix of jump one to the power of t, that is
Chapman–Kolmogorov_equation
Probability concept
n + 1, Pr(Xn+1=x∣Xn=xn). The same information is represented by the transition matrix from time n to time n + 1. However, Markov chains are frequently assumed
Discrete-time_Markov_chain
Solution of a state equation
+∫0t𝜱(t−τ)[𝐁𝐮(τ)+𝐄𝐰(τ)]dt where Φ(t) is the state transition matrix. The state-transition equation as derived above is useful only when the initial
State-transition_equation
Physical phenomenon
The mixture can be expressed as a ratio of matrix elements (Fermi's golden rule relates transitions to matrix elements) :y≡gFMFgGTMGT The interesting observation
Beta_decay_transition
Finds likely sequence of hidden states
S transition matrix input emit: S × M emission matrix input obs: sequence of T observations prob ← T × S matrix of zeroes prev ← empty T × S matrix for
Viterbi_algorithm
Aspect of mathematical queueing theory
there is no limit on the number of entities it can contain. The transition probability matrix for an M/D/1 queue with arrival rate λ and service time 1, such
M/D/1_queue
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
matrix — a non-negative matrix describing a stochastic process. The sum of entries of any row is one. Transition matrix — a matrix representing the probabilities
List_of_named_matrices
Type of mathematical equation
variables), the stability conditions that the two eigenvalues of the transition matrix A each have a negative real part are equivalent to the conditions
Matrix_differential_equation
Stochastic process used in biology to describe finite populations
by one at each time step, a transition exists only between state i and state i − 1, i and i + 1. Thus the transition matrix of the stochastic process is
Moran_process
Type of shift space studied in ergodic theory
topology defined below. Some subshifts can be characterized by a transition matrix, as above; such subshifts are then called subshifts of finite type
Subshift_of_finite_type
Mathematical function, in linear algebra
relative to B: A Matrix for T relative to B′: A′ Transition matrix from B′ to B: P Transition matrix from B to B′: P−1 Such that starting in the bottom
Linear_map
Relation of a matrix of variables between two points in time
and n if the transition matrix A is nonsingular then the Riccati equation can be solved analytically in terms of the eigenvalues of a matrix, although these
Matrix_difference_equation
In control theory, visible state of a system
(t,t_{0})\,dt} where φ {\displaystyle \varphi } is the state-transition matrix. It is possible to determine a unique x ( t 0 ) {\displaystyle x(t_{0})}
Observability
Type of probability distribution
except one which is absorbing. Reordering the states, the transition probability matrix of a terminating Markov chain with m {\displaystyle m} transient
Discrete phase-type distribution
Discrete_phase-type_distribution
Mathematical model of computation
probability pij. These probabilities can be exhibited in the form of a transition matrix — Kemeny et al. 1959, p. 384 Finite Markov-chain processes are also
Finite-state_machine
Networking protocol for real-time communication
Matrix (sometimes stylized as [matrix] or [m] for short) is an open standard and communication protocol for real-time communication. It aims to make real-time
Matrix_(protocol)
Probabilistic optimal control
in the transition matrix (giving the effect of current values of the state variables on their own evolution) and/or the control response matrix of the
Stochastic_control
Statistical Markov model
of transition probabilities for transitions from any given state must sum to 1. Thus, the N × N matrix of transition probabilities is a Markov matrix. Because
Hidden_Markov_model
Matrix consisting of linearly independent solutions to a linear differential equation
equation are of the form Ψ0(t)C. The fundamental matrix is used to express the state-transition matrix, an essential component in the solution of a system
Fundamental matrix (linear differential equation)
Fundamental_matrix_(linear_differential_equation)
Matrix representing the frequency of evolution of a protein or nucleotide sequence
In bioinformatics and evolutionary biology, a substitution matrix describes the frequency at which a character in a nucleotide sequence or a protein sequence
Substitution_matrix
Nonlinear equation which arises on linear optimal control problems
× n state transition matrix, B is the n × k matrix of control multipliers, Q (n × n) is a symmetric positive semi-definite state cost matrix, and R (k
Algebraic_Riccati_equation
that an irreducible, positive recurrent, aperiodic Markov chain with transition matrix P is reversible if and only if its stationary Markov chain satisfies
Kolmogorov's_criterion
Algorithm that estimates unknowns from a series of measurements over time
sigma points, and Wjc are the second-order weights. The matrix 𝐐k is the covariance of the transition noise, 𝐰k. Given prediction estimates 𝐱̂k∣k−1 and
Kalman_filter
continuous-time Markov chain with transition rate matrix Q, the uniformized discrete-time Markov chain has probability transition matrix P:=(pij)i,j, which is defined
Uniformization (probability theory)
Uniformization_(probability_theory)
American filmmakers
Sieczkowski, Cavan (July 30, 2012). "Larry Wachowski Transgender: 'Matrix' Director Reveals Transition To Lana Wachowski (VIDEO)". HuffPost. Archived from the original
The_Wachowskis
Compact station wagon by Toyota, 2002–2014
The Toyota Matrix, officially named Toyota Corolla Matrix, is a compact hatchback manufactured by Toyota Motor Manufacturing Canada in Cambridge, Ontario
Toyota_Matrix
Concept in control theory mathematics
τ ) {\displaystyle {\boldsymbol {\Phi }}(t,\tau )} is the state transition matrix of x ˙ = A ( t ) x {\displaystyle {\boldsymbol {\dot {x}}}={\boldsymbol
Controllability_Gramian
Simplified model of orbital relative motion
_{0}=\delta \mathbf {v} _{0}=\mathbf {0} } , since the full state transition matrix is nonsingular. In practice, rendezvous is achieved using impulsive
Clohessy–Wiltshire_equations
Unitary matrix containing information on the weak interaction
physics, the Cabibbo–Kobayashi–Maskawa matrix, CKM matrix, quark mixing matrix, or KM matrix is a unitary matrix that contains information on the strength
Cabibbo–Kobayashi–Maskawa matrix
Cabibbo–Kobayashi–Maskawa_matrix
Linear operator used in quantum mechanics
which serves the purpose of calculating transition probabilities between different quantum states. The matrix element considers the effect of the newly
Matrix_element_(physics)
Pattern defining an infinite sequence of numbers
absolute value. In the first-order matrix difference equation [xt−x∗]=A[xt−1−x∗] with state vector x and transition matrix A, x converges asymptotically to
Recurrence_relation
Standard example in game theory
strategy vector of Y (where the indices are from Y's point of view), a transition matrix M may be defined for X whose ij-th entry is the probability that the
Prisoner's_dilemma
Form of a matrix indicating its eigenvalues and their algebraic multiplicities
[⌜λ11⌝λ11⌞λ1⌟⌜λ21⌝⌞λ2⌟[λ3]⋱⌜λn1⌝⌞λn⌟] Example of a matrix in Jordan normal form. All matrix entries not shown are zero. The outlined squares are known
Jordan_normal_form
Formulation of quantum mechanics
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually
Matrix_mechanics
Cheeger bound is a bound of the second largest eigenvalue of the transition matrix of a finite-state, discrete-time, reversible stationary Markov chain
Cheeger_bound
Linear operator
polynomials. The theory of birth-death processes where the infinite transition matrix can be transformed into a self-adjoint Jacobi operator acting on the
Jacobi_operator
interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the
Rumor spread in social network
Rumor_spread_in_social_network
Transitional Literata Designer: Google & TypeTogether Class: Scotch, Old style Literaturnaya Designer: Anatolii Shchukin Class: Transitional Matrix (typeface)
List_of_serif_typefaces
Physical process of transition between basic states of matter
(31 January 2014). "Top eigenvalue of a random matrix: large deviations and third order phase transition". Journal of Statistical Mechanics: Theory and
Phase_transition
Geometric algorithm
and Mt gives the t-step transition matrix. We define the diffusion matrix L (it is also a version of graph Laplacian matrix) Li,j=k(xi,xj) We then define
Diffusion_map
In systems theory
(t,\sigma )B(\sigma )} where ϕ {\displaystyle \phi } is the state-transition matrix associated with the realization. System identification techniques
Realization_(systems)
Principle in kinetic systems
unique Markov transition matrix exists which is closest according to the stationary distribution and a given norm. The closest Matrix can be computed
Detailed_balance
Class of algorithms in information theory
write 𝐩 as (p1,p2,…,pn),∑i=1npi=1 Q=(qji) is a m×n matrix that behaves like a transition matrix from Y to X with respect to the channel law; that is
Blahut–Arimoto_algorithm
Mathematical theorem
lemma that gives upper and lower bounds to the norm of the state transition matrix. Bihari-LaSalle inequality, a nonlinear generalization of Grönwall's
Grönwall's_inequality
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
Type of physical quantity
bases, respectively, A =[Aik] is the transition matrix for the contravariant (upper) indices, B is the transition matrix for the covariant (lower) indices
Pseudotensor
Transition rate formula
needed for the transition. Only the magnitude of the matrix element ⟨f|H′|i⟩ enters the Fermi's golden rule. The phase of this matrix element, however
Fermi's_golden_rule
Concepts from linear algebra
available for clustering. A Markov chain is represented by a matrix whose entries are the transition probabilities between states of a system. In particular
Eigenvalues_and_eigenvectors
Study of evolutionary relationships between organisms
secondary-structure states and estimation of a 1-PAM secondary-structure transition matrix. The transition matrix enables maximum-likelihood structural phylogenetic tree
Phylogenetics
Calculation of complex statistical distributions
burn-in period nburn is calculated using eigenvalue analysis of the transition matrix to estimate the number of initial iterations needed for the Markov
Markov_chain_Monte_Carlo
Concept in machine learning
transition probability. To get smooth value approximation, diffusion wavelets are used. Krylov basis construction uses the actual transition matrix instead
Automatic basis function construction
Automatic_basis_function_construction
Procedure for recovering a blurred image
sources, thus the observed image can be represented in terms of a transition matrix p operating on an underlying image: d i = ∑ j p i , j u j , {\displaystyle
Richardson–Lucy_deconvolution
Arithmetic operation
steps. The matrix power An is the transition matrix between the state now and the state at a time n steps in the future. So computing matrix powers is
Exponentiation
Concept in linear algebra
^{r\times r}} is the transition matrix from B {\displaystyle B} to B ′ {\displaystyle B'} then with respect to B ′ {\displaystyle B'} the matrix Q − 1 M Q {\displaystyle
Reducing_subspace
Electron-positron scattering
Both the scattering and annihilation diagrams contribute to the transition matrix element. By letting k and k' represent the four-momentum of the positron
Bhabha_scattering
Predictive filter
specializations and simplifications. The discrete state transition matrix A is a square matrix of dimension 2, with all main diagonal terms equal to 1
Alpha_beta_filter
Time density of the average information in a stochastic process
defined on a countable number of states. Given its right stochastic transition matrix Pij and an entropy hi:=−∑jPijlogPij associated with each state, one
Entropy_rate
Homotopic map of a graph
topological representative f:Γ→Γ of an automorphism φ of Fk the transition matrix M(f) is an rxr matrix (where r is the number of topological edges of Γ) where
Train_track_map
commensurate order FDEs and a system of linear FDDEs are given by a state transition matrix. Doha, E.H.; Bhrawy, A.H.; Ezz-Eldien, S.S. (December 2011). "Efficient
Fractional Chebyshev collocation method
Fractional_Chebyshev_collocation_method
Measure in graph theory
Seeley's index is the stationary distribution of the Markov chain with transition matrix P {\displaystyle P} , that is, of the random walk that at each step
Seeley's_index
Canadian statistician
(now at York University), whose 1970 dissertation "The Choice Of Transition Matrix In Monte Carlo Sampling Methods Using Markov Chains" developed the
W._K._Hastings
Matrix of binary truth values
matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain B = {0, 1}. Such a matrix can
Logical_matrix
τ ) {\displaystyle {\boldsymbol {\Phi }}(t,\tau )} is the state transition matrix of x ˙ = A ( t ) x {\displaystyle {\boldsymbol {\dot {x}}}={\boldsymbol
Observability_Gramian
Dutch physicist (1894–1952)
Kramers did most of his doctoral research (on intensities of atomic transitions) in Copenhagen, he obtained his formal Ph.D. under Ehrenfest in Leiden
Hans_Kramers
Concept in genetics
by one, go down by one, or can stay the same. This means that the transition matrix is tridiagonal, which means that mathematical solutions are easier
Genetic_drift
Function acting on the space of physical states in physics
written in matrix form to map one basis vector to another. Since the operators are linear, the matrix is a linear transformation (aka transition matrix) between
Operator_(physics)
Range on the electromagnetic spectrum
than dipole transitions. Second, not all transitions have the same transition matrix element, absorption coefficient or oscillator strength. For some types
Absorption_band
Mathematical concept
of S→S. Each such map has a n×n matrix representation, called deterministic transition matrix. It is a binary matrix but it has exactly one entry 1 in
Random_dynamical_system
Reversible transition in amorphous materials
The glass–liquid transition, or glass transition, is the gradual and reversible transition in amorphous materials (or in amorphous regions within semicrystalline
Glass_transition
Pattern in control theory
\sigma )B(\sigma )} such that ϕ {\displaystyle \phi } is the state transition matrix. The weighting pattern will determine a system, but if there exists
Weighting_pattern
Formula for the probability that a system will change between two energy states
Landau–Zener theory is to determine elements of the scattering matrix and the transition probabilities between states of this model after evolution with
Landau–Zener_formula
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
Direct extension and penetration by cancer cells into neighboring tissues
the mesenchymal-amoeboid transition in cells in a 3D matrix. There exists the possibility of an amoeboid-mesenchymal transition that is the reverse process
Invasion_(cancer)
Method of analysis
involve placing hierarchical Dirichlet process priors over the HMM transition matrix. Step detection Keogh, Eamonn, et al. "Segmenting time series: A survey
Time-series_segmentation
Aspect of queueing theory
state i – 1, i, i + 1, i + 2, .... The embedded Markov chain has transition matrix P=(a0a1a2a3a4⋯a0a1a2a3a4⋯0a0a1a2a3⋯00a0a1a2⋯000a0a1⋯⋮⋮⋮⋮⋮⋱) where
M/G/1_queue
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TRANSITION MATRIX
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TRANSITION MATRIX
TRANSITION MATRIX
TRANSITION MATRIX
TRANSITION MATRIX
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TRANSITION MATRIX
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