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.
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.