enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. State-transition matrix - Wikipedia

    en.wikipedia.org/wiki/State-transition_matrix

    The state-transition matrix is used to find the solution to a general state-space representation of a linear system in the following form ˙ = () + (), =, where () are the states of the system, () is the input signal, () and () are matrix functions, and is the initial condition at .

  3. Stochastic matrix - Wikipedia

    en.wikipedia.org/wiki/Stochastic_matrix

    A substochastic matrix is a real square matrix whose row sums are all ; In the same vein, one may define a probability vector as a vector whose elements are nonnegative real numbers which sum to 1. Thus, each row of a right stochastic matrix (or column of a left stochastic matrix) is a probability vector.

  4. State-space representation - Wikipedia

    en.wikipedia.org/wiki/State-space_representation

    If the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form. [1] [2] The state-space method is characterized by the algebraization of general system theory, which makes it possible to use Kronecker vector-matrix structures.

  5. Transition matrix - Wikipedia

    en.wikipedia.org/wiki/Transition_matrix

    Change-of-basis matrix, associated with a change of basis for a vector space. Stochastic matrix , a square 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 an initial time t 0 {\displaystyle t_{0}} gives x {\displaystyle x} at a later time t ...

  6. Continuous-time Markov chain - Wikipedia

    en.wikipedia.org/wiki/Continuous-time_Markov_chain

    Transition graph with transition probabilities, exemplary for the states 1, 5, 6 and 8. There is a bidirectional secret passage between states 2 and 8. The image to the right describes a discrete-time Markov chain modeling Pac-Man with state-space {1,2,3,4,5,6,7,8,9}. The player controls Pac-Man through a maze, eating pac-dots.

  7. Balance equation - Wikipedia

    en.wikipedia.org/wiki/Balance_equation

    For a continuous time Markov chain (CTMC) with transition rate matrix, if can be found such that for every pair of states and π i q i j = π j q j i {\displaystyle \pi _{i}q_{ij}=\pi _{j}q_{ji}} holds, then by summing over j {\displaystyle j} , the global balance equations are satisfied and π {\displaystyle \pi } is the stationary ...

  8. Master equation - Wikipedia

    en.wikipedia.org/wiki/Master_equation

    The most familiar form of a master equation is a matrix form: =, where is a column vector, and is the matrix of connections. The way connections among states are made determines the dimension of the problem; it is either

  9. Substitution model - Wikipedia

    en.wikipedia.org/wiki/Substitution_model

    The equilibrium row vector π must be annihilated by the rate matrix Q: π Q = 0 . {\displaystyle \pi \,Q=0\,.} The transition matrix function is a function from the branch lengths (in some units of time, possibly in substitutions), to a matrix of conditional probabilities.