An introduction to semi-tensor product of matrices and its applications

著者

書誌事項

An introduction to semi-tensor product of matrices and its applications

Daizhan Cheng, Hongsheng Qi, Yin Zhao

World Scientific, c2012

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注記

Includes bibliographical references and index

内容説明・目次

内容説明

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.

目次

  • 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.

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