内容简介：

    本书介绍了一种矩阵普通乘法的扩展——矩阵的半张量积。它将矩阵普通乘法扩展到任意两个矩阵，并保持了所有矩阵普通乘法的基本性质。除此之外，它还拥有矩阵普通乘法所没有的性质——伪交换性。矩阵的半张量积是本书作者在处理高维数据和多线性映射时提出的。经过十多年的发展，半张量积已经成为处理非线性和逻辑运算的有力工具。

    本书综合介绍了半张量积的理论及其在逻辑函数、模糊控制、布尔网络、非线性系统分析与控制等多方面的应用。 本书具有如下特点：

1. 矩阵半张量积是一套新发展的工具，已被成功应用于布尔网络控制、电力系统控制等方面。同时，它还有着广泛的应用前景。
2. 本书是关于矩阵半张量积的第一本英文专著。
3. 本书包含大量例子与习题，可作为教材使用，尤其适合作为研究生教材和自学、研究参考书。
4. 本书是关于矩阵半张量积的标准参考书目，可供相关方向科研工作者及工程师使用。

英文目录：
Preface
Notations
1. Multi-Dimensional Data
   1.1 Multi-Dimensional Data
   1.2 Arrangement of Data
   1.3 Matrix Products
      1.3.1 Kronecker Product of Matrices
      1.3.2 Hadamard Product
      1.3.3 Khatri-Rao Product
   1.4 Tensor
   1.5 Nash Equilibrium
   1.6 Symmetric Group
   1.7 Swap Matrix
   Exercises
2. Semi-Tensor Product of Matrices
   2.1 Multilinear Function
   2.2 Left Semi-Tensor Product of Matrices
   2.3 Fundamental Properties
   2.4 Pseudo-Commutativity via Swap Matrix
   2.5 Semi-Tensor Product as Bilinear Mapping
   Exercises
3. Multilinear Mappings among Vector Spaces
   3.1 Cross Product on R³
   3.2 General Linear Algebra
   3.3 Mappings over Matrices
   3.4 Converting Matrix Expressions
   3.5 Two Applications
      3.5.1 General Linear Group and Its Algebra
      3.5.2 Hautus and Sylvester Equations
   Exercises
4. Right and General Semi-Tensor Products
   4.1 Right STP
   4.2 Semi-Tensor Product of Arbitrary Matrices
   Exercises
5. Rank, Pseudo-Inverse, and Positivity of STP 101
   5.1 Rank of Products
   5.2 Pseudo-Inverse of STP
      5.2.1 Moore-Penrose Inverse
      5.2.2 Drazin Inverse
   5.3 Positivity of Products
   Exercises
6. Matrix Expression of Logic
   6.1 Logic and Its Expression
   6.2 General Structure of Logical Operators
   6.3 Fundamental Properties of Logical Operators
   6.4 Logical System and Logical Inference
   6.5 Multi-Valued Logic
   Exercises
7. Mix-Valued Logic
   7.1 Normal Form of Logical Operators
   7.2 Mix-Valued Logic
   7.3 General Logical Mappings
   7.4 Two Practical Examples
      7.4.1 Mix-Valued Logical Form of Rules in Fuzzy Control
      7.4.2 Expression of Strategies of Dynamic Games
   Exercises
8. Logical Matrix, Fuzzy Set and Fuzzy Logic
   8.1 Matrices of General Logical Variables
   8.2 Logical Operators for k-Valued Matrices
   8.3 Fuzzy Sets
   8.4 Mappings over Fuzzy Sets
   8.5 Fuzzy Logic and Its Computation
   Exercises
9. Fuzzy Relational Equation
   9.1 k-Valued Matrix and Fuzzy Relational Equations
   9.2 Structure of the Set of Solutions
   9.3 Solving Fuzzy Relational Equation
   9.4 Numerical Examples
   Exercises
10. Fuzzy Control with Coupled Fuzzy Relations
   10.1 Multiple Fuzzy Relations
      10.1.1 Matrix Expression
      10.1.2 Multiple Fuzzy Inference
      10.1.3 Compounded Multiple Fuzzy Relations
   10.2 Fuzzy Control of Coupled Multiple Fuzzy Relations
      10.2.1 Fuzzification via Dual Fuzzy Structure
      10.2.2 Design of Fuzzy Controller
      10.2.3 Defuzzification
   10.3 Numerical Solution for Fuzzy Control Design
   Exercises
11. Representation of Boolean Functions
   11.1 Boolean Functions in Galois Field Z2
   11.2 Polynomial Form of Boolean Functions
   11.3 Walsh Transformation
   11.4 Linear Structure
   11.5 Nonlinearity
   11.6 Symmetry of Boolean Function
   Exercises
12. Decomposition of Logical Functions
   12.1 Disjoint Bi-Decomposition
   12.2 Non-Disjoint Bi-Decomposition
   12.3 Decomposition of Multi-Valued Logical Functions
   12.4 Decomposition of Mix-Valued Logical Functions
   Exercises
13. Boolean Calculus
   13.1 Boolean Derivatives
   13.2 Boolean Differential Equations
   13.3 Boolean Integral
      13.3.1 Primitive Function
      13.3.2 Indefinite Integral
      13.3.3 Definite Integral
   Exercises
14. Lattice, Graph, and Universal Algebra
   14.1 Lattice
   14.2 Isomorphic Lattices and Sublattices
   14.3 Matrix Expression of Finite Lattice
   14.4 Distributive and Modular Lattices
   14.5 Graph and Its Adjacency Matrix
   14.6 Vector Space Structure of Graph
   14.7 Planar Graph and Coloring Problem
   14.8 Universal Algebra
   14.9 Lattice-Based Logics
   Exercises
15. Boolean Network
   15.1 An Introduction
   15.2 Fixed Points and Cycles
   15.3 Invariant Subspace and Input-State Description
      15.3.1 State Space and Subspaces
      15.3.2 Input-State Description
   15.4 Higher-Order Boolean Networks
      15.4.1 First Algebraic Form of Higher-Order Boolean Networks
      15.4.2 Second Algebraic Form of Higher-Order Boolean Networks
   15.5 Dynamic-Static Boolean Networks
   Exercises
16. Boolean Control System
   16.1 Dynamics of Boolean Control Networks
   16.2 Controllability
   16.3 Observability
   16.4 Disturbance Decoupling
   16.5 Some Other Control Problems
      16.5.1 Stability and Stabilization
      16.5.2 Optimal Control
      16.5.3 Identification
   Exercises
17. Game Theory
   17.1 An Introduction to Game Theory
   17.2 Infinitely Repeated Games
   17.3 Local Optimization of Strategies and Local Nash/Sub-Nash Equilibrium
   Exercises
18. Multi-Variable Polynomials
   18.1 Matrix Expression of Multi-Variable Polynomials
   18.2 Differential Form of Functional Matrices
   18.3 Conversion of Generators
   18.4 Taylor Expansion of Multi-Variable Functions
   18.5 Fundamental Formula of Differential
   18.6 Lie Derivative
   Exercises
19. Some Applications to Differential Geometry and Algebra
   19.1 Calculation of Connection
   19.2 Contraction of Tensor Field
   19.3 Structure Matrix of Finite-Dimensional Algebra
   19.4 Two-Dimensional Algebras
   19.5 Three-Dimensional Algebras
   19.6 Lower-Dimensional Lie Algebra and Invertible Algebra
   19.7 Tensor Product Algebra
   Exercises
20. Morgan's Problem
   20.1 Input-Output Decomposition
   20.2 Problem Formulation
   20.3 Numerical Expression of Solvability
   Exercises
21. Linearization of Nonlinear Control Systems
   21.1 Carleman Linearization
   21.2 First Integral
   21.3 Invariance of Polynomial System
   21.4 Feedback Linearization of Nonlinear Control System
   21.5 Single Input Feedback Linearization
   21.6 Algorithm for Non-Regular Feedback Linearization
   Exercises
22. Stability Region of Dynamic Systems
   22.1 Stability Region
   22.2 Stable Submanifold
   22.3 Quadratic Approximation
   22.4 Higher Order Approximation
   22.5 Differential-Algebraic System
   Exercises
Appendix A Numerical Algorithms
   A.1 Basic Functions
   A.2 Some Examples
Bibliography
Index