Paper Title
A Brief Tutorial Exposition Of Semi-Tensor Products Of Matrices

Abstract
This paper is a brief tutorial exposition of a novel and highly-useful product of matrices called the semi-tensor product (STP) or Cheng product. This new product allows the multiplication of two matrices A_mn and B_pq that do not satisfy the conformity condition required in a conventional matrix product (CMP), namely, that the column dimension n of the first matrix A be equal to the row dimension q of the second matrix B. The STP inherits almost all of the properties of the CMP, and reduces to it when n = q. The basic concepts and properties of the STP are presented, and demonstrated via tutorial illustrative examples. Applications of the STP include multi-linear and non-linear control problems, theoretical analysis of mathematical problems, derivation of mathematical proofs, and matrix expression of Boolean functions as well as pseudo-Boolean functions. Keywords- Matrices, Semi-Tensor Products, Non-Conformity, Multiple-dimension Case, Property Inheritance, Boolean Functions, Pseudo-Boolean Functions.