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Describes state evolution of a linear system
the state-transition matrix is a matrix function that describes how the state of a linear system changes over time. Essentially, if the system's state is
State-transition_matrix
Topics referred to by the same term
matrix used to describe the transitions of a Markov chain. State-transition matrix, a matrix whose product with the state vector x {\displaystyle x} at
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
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
Dynamic system property
(t)+D(t)\mathbf {u} (t).\end{aligned}}} The state-transition matrix ϕ is also smooth. Introduce the n × m matrix-valued function M0(t) = ϕ(t0, t)B(t) and
Controllability
Table in automata theory and sequential logic
logic, a state-transition table is a table showing what state (or states in the case of a nondeterministic finite automaton) a finite-state machine will
State-transition_table
Random process independent of past history
associated with various state changes are called transition probabilities. The process is characterized by a state space, a transition matrix describing the probabilities
Markov_chain
Solution of a state equation
)+\mathbf {Ew} (\tau )]dt\end{aligned}}} where Φ(t) is the state transition matrix. The state-transition equation as derived above is useful only when the initial
State-transition_equation
Nonlinear equation which arises on linear optimal control problems
n × 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
Algebraic_Riccati_equation
Matrix consisting of linearly independent solutions to a linear differential equation
{\displaystyle \Psi _{0}(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)
t , τ ) {\displaystyle {\boldsymbol {\Phi }}(t,\tau )} is the state transition matrix of x ˙ = A ( t ) x {\displaystyle {\boldsymbol {\dot {x}}}={\boldsymbol
Observability_Gramian
Concept in control theory mathematics
t , τ ) {\displaystyle {\boldsymbol {\Phi }}(t,\tau )} is the state transition matrix of x ˙ = A ( t ) x {\displaystyle {\boldsymbol {\dot {x}}}={\boldsymbol
Controllability_Gramian
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
Observability
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
Mathematical theorem
Grönwall's 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 function often applied to matrices
are similar to those obtained using Grönwall's lemma. Thus the state transition matrix Φ ( t , t 0 ) {\displaystyle \Phi (t,t_{0})} associated with a
Logarithmic_norm
Simplified model of orbital relative motion
{r} _{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
Predictive filter
following specializations and simplifications. The discrete state transition matrix A is a square matrix of dimension 2, with all main diagonal terms equal to
Alpha_beta_filter
Probabilistic optimal control
transition matrix (giving the effect of current values of the state variables on their own evolution) and/or the control response matrix of the state
Stochastic_control
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)
In systems theory
)=C(t)\phi (t,\sigma )B(\sigma )} where ϕ {\displaystyle \phi } is the state-transition matrix associated with the realization. System identification techniques
Realization_(systems)
Physical process of transition between basic states of matter
chemistry and biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly
Phase_transition
in a multiport system. State transition matrix — exponent of state matrix in control systems. Substitution matrix — a matrix from bioinformatics, which
List_of_named_matrices
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)
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
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
stable multidimensional LTI system with the state-transition matrix A {\displaystyle A} and input matrix B {\displaystyle B} , it was shown in [CK06]
Quantized state systems method
Quantized_state_systems_method
Algorithm that estimates unknowns from a series of measurements over time
Schmidt–Kalman filter Separation principle Sliding mode control State-transition matrix Stochastic differential equations Switching Kalman filter Lacey
Kalman_filter
Pattern in control theory
(t,\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
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
Paradox of combining strategies
is a Markov chain, and an analysis of its state transition matrix (again with M=3) shows that the steady state probability of using coin 2 is 0.3836, and
Parrondo's_paradox
Algorithm in mathematics
stochastic transition matrix A = { a i j } = P ( X t = j ∣ X t − 1 = i ) . {\displaystyle A=\{a_{ij}\}=P(X_{t}=j\mid X_{t-1}=i).} The initial state distribution
Baum–Welch_algorithm
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
Reversible transition in amorphous materials
brittle "glassy" state into a viscous or "rubbery" state as the temperature is increased. An amorphous solid that exhibits a glass transition is called a glass
Glass_transition
Probability concept
{\text{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: [ 0 1 2 1 2
Continuous-time_Markov_chain
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)
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
Concept in probability theory
Markov processes plays the role that the transition matrix does in the theory of Markov processes with a finite state space. Let ( X , A ) {\displaystyle (X
Markov_kernel
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
Transition rate formula
measurement is much larger than the time needed for the transition. Only the magnitude of the matrix element ⟨ f | H ′ | i ⟩ {\displaystyle \langle f|H'|i\rangle
Fermi's_golden_rule
Physical phenomenon
In nuclear physics, a beta decay transition is the change in state of an atomic nucleus undergoing beta decay. A beta particle and a neutrino are emitted
Beta_decay_transition
Family of zinc-dependent metalloendopeptidases
Matrix metalloproteinases (MMPs), also known as matrix metallopeptidases or matrixins, are metalloproteinases that are calcium-dependent zinc-containing
Matrix_metalloproteinase
Concept in physics
1 shows the typical line shape for electronic transitions of individual chromophores in a solid matrix. The zero-phonon line is located at a frequency
Zero-phonon line and phonon sideband
Zero-phonon_line_and_phonon_sideband
Equations governing time evolution of physical systems
given time, and the switching between states is determined by a transition rate matrix. The equations are a set of differential equations – over time –
Master_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
dynamical system can be written in terms of a semigroup operator, or state transition matrix, S : H → H {\displaystyle S:H\to H} such that u ( t ) = S ( t )
Inertial_manifold
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)
1\right)} where the 2x2 transfer matrix Wj of the jth residue equals the matrix of statistical weights for the state transitions W j = [ s j 1 σ j s j 1 ] {\displaystyle
Zimm–Bragg_model
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
Probabilistic numerical ODE solver
higher-order derivatives. F {\displaystyle F} is a state transition matrix, L {\displaystyle L} a diffusion matrix, and B ( t ) {\displaystyle B(t)} is a vector
ODE_filter
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
Formula for the probability that a system will change between two energy states
analytic solution to the equations of motion governing the transition dynamics of a two-state quantum system, with a time-dependent semi-classical Hamiltonian
Landau–Zener_formula
includes the probability of a given transition into the transition function, turning it into a transition matrix. Thus, the probabilistic automaton also
Probabilistic_automaton
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
Formal constraint in quantum mechanics
chemistry, a selection rule, or transition rule, formally constrains the possible transitions of a system from one quantum state to another. Selection rules
Selection_rule
Dimensionless quantity in spectroscopy
electromagnetic radiation in transitions between energy levels of an atom or molecule. For example, if an emissive state has a small oscillator strength
Oscillator_strength
Probability concept
steady-state distribution. Even with time-inhomogeneous Markov chains, where multiple transition matrices are used, if each such transition matrix exhibits
Discrete-time_Markov_chain
Mathematical model of computation
in state si it moves on to the next stop to state sj with probability pij. These probabilities can be exhibited in the form of a transition matrix — Kemeny
Finite-state_machine
Effect of an electron's interaction with the electromagnetic field
time-dependent perturbation theory, one finds that the most likely transitions of the electron from one state to the other occur due to the summand of W ( t ) {\displaystyle
Electric_dipole_transition
so-called scattering matrix (S-matrix). The probability amplitude for a transition of a quantum system from the initial state having state vector | i ⟩ {\displaystyle
Initial and final state radiation
Initial_and_final_state_radiation
continuous-time Markov chain with transition rate matrix Q, the uniformized discrete-time Markov chain has probability transition matrix P := ( p i j ) i , j {\displaystyle
Uniformization (probability theory)
Uniformization_(probability_theory)
consecutive residues. However, the simple nature of the coil state allows this to be reduced to a 3x3 matrix for most applications. The Zimm–Bragg and Lifson–Roig
Lifson–Roig_model
Quantum analog of probabilistic automata
adjacency matrix indicates how any given state (row in the state vector) will transition to the next state; a state transition is given by matrix multiplication
Quantum_finite_automaton
Search for an atomic arrangement with the lowest inter-atomic force
following: ∂E/∂r = 0 and the Hessian matrix, ∂∂E/∂ri∂rj, has exactly n negative eigenvalues. Algorithms to locate transition state geometries fall into two main
Energy_minimization
Statistical Markov model
N^{2}} transition probabilities. The set of transition probabilities for transitions from any given state must sum to 1. Thus, the N × N matrix of transition
Hidden_Markov_model
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
Irreducible representation of the rotation group SO
The Wigner D-matrix is a unitary matrix in an irreducible representation of the groups SU(2) and SO(3). It was introduced in 1927 by Eugene Wigner, and
Wigner_D-matrix
Examples of the probabilistic construct
day 1 (tomorrow) can be predicted by multiplying the state vector from day 0 by the transition matrix: x ( 1 ) = x ( 0 ) P = [ 1 0 ] [ 0.9 0.1 0.5 0.5 ]
Examples_of_Markov_chains
dimensionality of the state estimate, while still considering the effects of the additional state in the calculation of the covariance matrix and the Kalman
Schmidt–Kalman_filter
Mathematical technique
including the Zimm–Bragg and Lifson–Roig models of the helix-coil transition, transfer matrix models for protein-DNA binding, as well as the famous exact solution
Transfer-matrix method (statistical mechanics)
Transfer-matrix_method_(statistical_mechanics)
Model of quantum computation
machines in a framework based on transition matrices. That is, a matrix can be specified whose product with the matrix representing a classical or probabilistic
Quantum_Turing_machine
Pictorial representation of the behavior of subatomic particles
to the final state, in terms of either particles or fields. The transition amplitude is then given as the matrix element of the S-matrix between the initial
Feynman_diagram
Mechanism of beta decay proposed in 1933
of the neutrino and β {\displaystyle \beta } is the Dirac matrix. Noting that the transition probability has a sharp maximum for values of p σ {\displaystyle
Fermi's_interaction
Loss of quantum coherence
described by a density matrix ρ {\displaystyle \rho } in a particular state | ϕ ⟩ {\displaystyle |\phi \rangle } , i.e. the transition probability mentioned
Quantum_decoherence
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
Form of a matrix indicating its eigenvalues and their algebraic multiplicities
x} is a chain of length two corresponding to the eigenvalue 4. The transition matrix P such that P−1AP = J is formed by putting these vectors next to each
Jordan_normal_form
Canadian actor (born 1964)
(1997) was well received. Greater stardom came with his role as Neo in The Matrix (1999); Until 2016, Reeves was the highest paid actor for a single production
Keanu_Reeves
Chemical compound
oxidation state mercury normally attains is +2, and for this reason it is sometimes considered a post-transition metal instead of a transition metal. HgF4
Mercury(IV)_fluoride
in a matrix. The keyboard controller, often an 8-bit processor, parses columns one-by-one and recovers the state of 8 keys at once. This matrix scan process
Computer security compromised by hardware failure
Computer_security_compromised_by_hardware_failure
Soviet theoretical physicist (1908–1968)
His accomplishments include the independent co-discovery of the density matrix method in quantum mechanics (alongside John von Neumann), the quantum mechanical
Lev_Landau
m),} where q(i,j) is the transition rate from state i to state j. Similarly, for a stochastic matrix P, P is a lumpable matrix on a partition T if and
Lumpability
Peacekeeping mission, 1992–1993
The United Nations Transitional Authority in Cambodia (UNTAC) was a United Nations administrative and peacekeeping operation in Cambodia in 1992–93 formed
United Nations Transitional Authority in Cambodia
United_Nations_Transitional_Authority_in_Cambodia
Linear operator
Jacobi, dating to 1848, stating that every symmetric matrix over a principal ideal domain is congruent to a tridiagonal matrix. The most important case
Jacobi_operator
Type of mathematical equation
In the n = 2 case (with two state variables), the stability conditions that the two eigenvalues of the transition matrix A each have a negative real part
Matrix_differential_equation
Quantum logic gate
\\|ee0\rangle &&-i|ge1\rangle &&-i|ge1\rangle &&-|ee0\rangle \end{matrix}},} that is, the state ee acquires a phase − 1 {\displaystyle -1} the other three states
Cirac–Zoller controlled-NOT gate
Cirac–Zoller_controlled-NOT_gate
Quantum
finite-dimensional system, or a thermal state in infinite dimensional systems. For any differentiable parametrization of the density matrix ϱ ( θ ) {\displaystyle \varrho
Quantum_Fisher_information
Physics phenomenon
'ensemble' and describes it by a density matrix, which is a positive-semidefinite matrix, or a trace class when the state space is infinite-dimensional, and
Quantum_entanglement
Mathematical entity to describe the probability of each possible measurement on a system
quantum state. A mixed state for electron spins, in the density-matrix formulation, has the structure of a 2 × 2 {\displaystyle 2\times 2} matrix that is
Quantum_state
Filter for nonlinear state estimation
the case of well defined transition models, the EKF has been considered the de facto standard in the theory of nonlinear state estimation, navigation systems
Extended_Kalman_filter
Random matrix with gaussian entries
In random matrix theory, the Gaussian ensembles are specific probability distributions over self-adjoint matrices whose entries are independently sampled
Gaussian_ensemble
(weight percent exceeding 15%), the ELP transition from a linear state to a spherical aggregate state above the transition temperature is arrested, leading to
Elastin-like_polypeptides
Physical process
of crystalline solids. While a glass transition occurs when the liquid state is cooled, the jamming transition happens when the density, or the packing
Jamming_(physics)
Stochastic matrix representing links between entities
and 0 otherwise; this is the adjacency matrix of links. A related matrix S corresponding to the transitions in a Markov chain of given network is constructed
Google_matrix
Type of state in thermal systems
encounter complications like phase transitions or spontaneous symmetry breaking. The density matrix of a thermal state is given by ρ β , μ = e − β ( H −
KMS_state
Type of animal embryonic connective tissue
enabling mesenchyme to migrate along the extracellular matrix (ECM). Epithelial–mesenchymal transition occurs in embryonic cells that require migration through
Mesenchyme
Memoryless continuous-time stochastic process that shows two distinct values
_{1}&\lambda _{2}\\\lambda _{1}&-\lambda _{2}\end{pmatrix}}} is the transition rate matrix. The formal solution is constructed from the initial condition P
Telegraph_process
Concepts from linear algebra
non-negative, and every row of the matrix sums to one, being the sum of probabilities of transitions from one state to some other state of the system. The Perron–Frobenius
Eigenvalues_and_eigenvectors
Actor (born 1960)
Desert (1994), and more widely known as Agent Smith in the first three The Matrix films (1999–2003) and Elrond in The Lord of the Rings trilogy (2001–2003)
Hugo_Weaving
Finds likely sequence of hidden states
of each state input trans: S × S transition matrix input emit: S × M emission matrix input obs: sequence of T observations prob ← T × S matrix of zeroes
Viterbi_algorithm
Type of electric dipole moment
The transition dipole moment or transition moment, usually denoted d n m {\displaystyle \mathbf {d} _{nm}} for a transition between an initial state, m
Transition_dipole_moment
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