An introduction to semi-tensor product of matrices and its applications
- Cheng, Daizhan.
- Hackensack, N.J. : World Scientific, c2012.
- Physical description
- xxii, 587 p. : ill ; 24 cm.
QA329 .C476 2012
- Unknown QA329 .C476 2012
- Includes bibliographical references (p. 573-581) and index.
- Multi-Dimensional Data-- Semi-Tensor Product of Matrices-- Multilinear Mappings Among Vector Spaces-- Right and General Semi-Tensor Products-- Rank, Pseudo-Inverse, and Positivity of STP-- Matrix Expression of Logic-- Mix-Valued Logic-- Logical Matrix, Fuzzy Set and Fuzzy Logic-- Fuzzy Relational Equation-- Fuzzy Control with Coupled Fuzzy Relations-- Boolean Function with Galois Field Structure-- Decomposition of Logical Functions-- Boolean Calculus-- Lattice, Graph, and Universal Algebra-- Boolean Network-- Boolean Control System-- Game Theory-- Multi-Variable Polynomials-- Some Applications to Differential Geometry and Algebra-- Morgan's Problem-- Linearization of Nonlinear Control Systems-- Stability Region of Dynamic System.
- (source: Nielsen Book Data)
- Publisher's Summary
- In this title, a generalization of Conventional Matrix Product (CMP), called the Semi-Tensor Product (STP), is proposed. It extends the CMP to two arbitrary matrices and maintains all fundamental properties of CMP. In addition, it has a pseudo-commutative property, which makes it more superior to CMP. The STP was proposed by the authors to deal with higher-dimensional data as well as multilinear mappings. After over a decade of development, STP has been proven to be a powerful tool in dealing with nonlinear and logical calculations. This book is a comprehensive introduction to the theory of STP and its various applications, including logical function, fuzzy control, Boolean networks, analysis and control of nonlinear systems, amongst others.
(source: Nielsen Book Data)
- Publication date
- Daizhan Cheng, Hongsheng Qi, Yin Zhao.