It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix. The stochastic matrix was first developed by Andrey Markov...

probability and combinatorics, a doubly stochastic matrix (also called bistochastic matrix) is a square matrix X = ( x i j ) {\displaystyle X=(x_{ij})}...

identity matrix of size n, and 0n,n is the zero matrix of size n×n. Multiplying together stochastic matrices always yields another stochastic matrix, so Q...

A Google matrix is a particular stochastic matrix that is used by Google's PageRank algorithm. The matrix represents a graph with edges representing links...

Regular matrix may refer to: Regular stochastic matrix, a stochastic matrix such that all the entries of some power of the matrix are positive The opposite...

orthogonal matrix Precision matrix — a symmetric n×n matrix, formed by inverting the covariance matrix. Also called the information matrix. Stochastic matrix —...

Stochastic matrix Suhov & Kelbert 2008, Definition 2.1.1. Asmussen, S. R. (2003). "Markov Jump Processes". Applied Probability and Queues. Stochastic...

and sum up to one. Stochastic matrices are used to define Markov chains with finitely many states. A row of the stochastic matrix gives the probability...

word stochastic is used to describe other terms and objects in mathematics. Examples include a stochastic matrix, which describes a stochastic process...

An n × n matrix P is doubly stochastic precisely if both P and its transpose PT are stochastic matrices. A stochastic matrix is a square matrix of nonnegative...

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...

move to a different state as specified by the probabilities of a stochastic matrix. An equivalent formulation describes the process as changing state...

as a stochastic kernel or probability kernel) is a map that in the general theory of Markov processes plays the role that the transition matrix does in...

dissimilarity between compared sequences. It is an application of a stochastic matrix. Substitution matrices are usually seen in the context of amino acid...

of non-negative matrices, e.g. stochastic matrix; doubly stochastic matrix; symmetric non-negative matrix. Metzler matrix Berman, Abraham; Plemmons, Robert...

probability distributions Regular stochastic matrix, a stochastic matrix such that all the entries of some power of the matrix are positive Free regular set...

{\displaystyle \mathbb {F} } . A stochastic matrix is a real matrix of nonnegative entries, such that the sum of each column is one. Stochastic matrices include the...

elements of the probability vector. Stochastic matrix Dirichlet distribution Jacobs, Konrad (1992), Discrete Stochastics, Basler Lehrbücher [Basel Textbooks]...

will yield a doubly stochastic matrix, whose row sums and column sums equal to unity. However, unlike the doubly stochastic matrix, the diagonal sums of...

network Markov number Markov property Markov process Stochastic matrix (also known as Markov matrix) Subjunctive possibility (Russian: Андре́й Андре́евич...

covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the...

be described by a stochastic matrix, which lists the probabilities of moving to each state from any individual state. From this matrix, the probability...

{x} )} is the diagonal matrix of vector x {\displaystyle \mathbf {x} } . N {\displaystyle \mathbf {N} } is a row-stochastic matrix. The normalized eigenvector...

theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian, is a matrix representation of a...

In probability theory and related fields, a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random...

Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e...

stochastic vector, since the product of any two stochastic matrices is a stochastic matrix, and the product of a stochastic vector and a stochastic matrix...

time t realization of the stochastic n × n state transition matrix, Bt is the time t realization of the stochastic n × k matrix of control multipliers,...

possible that none of these will be positive. A row (column) stochastic matrix is a square matrix each of whose rows (columns) consists of non-negative real...

denoted A and B is a doubly stochastic matrix D such that DA = BD. If the doubly stochastic matrix is a permutation matrix, then it constitutes a graph...