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3D Shape Registration Using Spectral Graph Embedding and Probabilistic Matching
Published in Olivier Lézoray, Leo Grady, Image Processing and Analysis with Graphs, 2012
Avinash Sharma, Radu Horaud, Diana Mateus
A non-negative matrix A is a matrix such that all its entries are non-negative. A non-negative matrix with the property that all its row sums are +1 is said to be a (row) stochastic matrix. Acolumn stochastic matrix is the transpose of a row stochastic matrix. A stochastic matrix A with the property that A⊤ is also stochastic is said to be doubly stochastic: all row and column sums are +1 and aij ≥ 0. The set of stochastic matrices is a compact convex set with the simple and important property that A is stochastic if and only if A1=1, where 1 is the vector with all components equal to +1.
Linear Algebra
Published in Erchin Serpedin, Thomas Chen, Dinesh Rajan, Mathematical Foundations for SIGNAL PROCESSING, COMMUNICATIONS, AND NETWORKING, 2012
Fatemeh Hamidi Sepehr, Erchin Serpedin
An n × n matrix A = [αk,l] is called stochastic (probabilistic or transition) matrix if all its entries are non-negative (ak,l ≥ 0) and the entries in each row add up to one ∑l=1nak,l=1 A stochastic matrix can be interpreted as the transition probability matrix in a Markov chain, and its use arises in many fields such as probability, statistics, computer science, optimization (majorization theory), etc. A matrix with non-negative entries and with each column summing up to one is also referred to as a stochastic matrix. A doubly stochastic matrix is a matrix with non-negative entries, and in which each row and each column add up to one.
Matrices
Published in James R. Kirkwood, Bessie H. Kirkwood, Elementary Linear Algebra, 2017
James R. Kirkwood, Bessie H. Kirkwood
A stochastic matrix is a square matrix whose entries are nonnegative and each row sums to 1. Show that if A=a11a12a21a22andB=b11b12b21b22 are stochastic matrices, then AB is a stochastic matrix. Can you generalize this to larger stochastic matrices?
A community partitioning algorithm based on network enhancement
Published in Connection Science, 2021
Junjie Hu, Zhanquan Wang, Jiequan Chen, Yonghui Dai
Stochastic matrix is a matrix used to describe the transformation of a Markov chain, each term of which is a non-negative real number representing the probability. If a matrix s a doubly stochastic matrix (Wang et al., 2016), the following conditions shall be met: These two conditions guarantee that every term in a doubly stochastic matrix is a non-negative probability value and that the sum of every row and column is 1. Symmetric doubly stochastic matrix is a symmetric constraint added on the basis of the doubly stochastic matrix, namely , where represents the transpose of the matrix . Symmetric doubly stochastic matrix has the following properties: It has the maximum eigenvalue 1, and the corresponding eigenvector is All eigenvalues are non-negativeIt has n linearly independent eigenvectors
Consensus of hybrid multi-agent systems with heterogeneous dynamics
Published in International Journal of Control, 2020
Qi Zhao, Yuanshi Zheng, Yunru Zhu
In this paper, the communication relationship between agents is described by a weighted directed graph with a vertex set , an edge set and a nonnegative matrix . The neighbour set of the agent i is . A directed path between two distinct vertices and is a finite-ordered sequence of distinct edges of with the form . The degree matrix is a diagonal matrix with and the Laplacian matrix of the graph is defined as . A nonnegative matrix is said to be a (row) stochastic matrix if all its row sums are 1. A stochastic matrix is called indecomposable and aperiodic (SIA) if , where y is some column vector.
An overview of the consensus problem in the control of multi-agent systems
Published in Automatika, 2018
Rawad Abdulghafor, Shahrum Shah Abdullah, Sherzod Turaev, Mohamed Othman
A stochastic matrix is defined as a square matrix where all entries are nonnegative and representing some probabilities. However, the matrix is called doubly stochastic if all its entry elements are nonnegative and each column or each row sums up to one [112]. It is also termed as probability matrix, transition matrix, stationary matrix, substitution matrix, or Markov matrix.