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stochastic matrices: A right stochastic matrix is a square matrix of nonnegative real numbers, with each row summing to 1. A left stochastic matrix is...

Thus, a doubly stochastic matrix is both left stochastic and right stochastic. Indeed, any matrix that is both left and right stochastic must be square:...

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,...

row of P sums to one and all elements are non-negative, P is a right stochastic matrix. A stationary distribution π is a (row) vector, whose entries are...

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

no isolated vertices, then D + A {\displaystyle D^{+}A} right stochastic and hence is the matrix of a random walk, so that the left normalized Laplacian...

communities exactly. The community sizes and probability matrix may be known or unknown. Stochastic block models exhibit a sharp threshold effect reminiscent...

In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column...

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

1 (thus the matrix is both left stochastic and right stochastic) Fisher information matrix — a matrix representing the variance of the partial derivative...

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

trace of a square matrix A, denoted tr(A), is defined to be the sum of elements on the main diagonal (from the upper left to the lower right) of A. The trace...

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...

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...

complicated version of the matrix geometric method and is the classical solution method for M/G/1 chains. An M/G/1-type stochastic matrix is one of the form P...

\left[\mathbf {X} \mathbf {X} ^{\rm {T}}\right]} where T {\displaystyle {}^{\rm {T}}} denotes the transposed matrix of dimensions n × n {\displaystyle n\times...

the derivative as approximating linear mapping. Matrix calculus is used for deriving optimal stochastic estimators, often involving the use of Lagrange...

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...

algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions;...

statistics, given two stochastic processes { X t } {\displaystyle \left\{X_{t}\right\}} and { Y t } {\displaystyle \left\{Y_{t}\right\}} , the cross-covariance...