矩阵半张量积的基本原理与适用领域  

PRINCIPLE AND RANGE OF POSSIBLE APPLICATIONS OF SIME-TENSOR PRODUCT OF MATRICES

作　　者：程代展[1] 齐洪胜[1] 

机构地区：[1]中国科学院数学与系统科学研究院系统科学研究所系统控制重点实验室,北京100190

出　　处：《系统科学与数学》2012年第12期1488-1496,共9页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(61074114;60821091;61104065)资助项目

摘　　要：作为一种新的矩阵乘法,矩阵半张量积正得到国内外学者越来越多的重视和参与,从而使之应用于越来越多的研究课题中.希望分析矩阵半张量积的基本原理,从其合理性说明它产生的必然性和存在的意义.同时,与已有的综述不同,这里不准备具体介绍它在那些问题中得到那些应用,而是从原理出发,说明它可能在那些类型的相关科学问题中得到应用.这使我们能够更主动地去开发它可能的潜在应用.As a new matrix product, semi-tensor product of matrices has attracted more and more attention and participation from domestic and international academic society, and it has been applied to more and more research topics. The purpose of this paper is to analyze the fundamental principle of semi-tensor product, and to explain the reason for the emergence and existence of the semi-tensor product. Unlike the existing surveys, this paper does not intend to introduce what applications the semi- tensor product has been used to. Instead, we want to explore what kind of problems the semi-tensor product might be used according to the essence of semi-tensor product. Such observation could help us to dig out unknown possible further applications of semi-tensor product.

关 键 词：矩阵半张量积 布尔网络 泛代数 多元多项式 非线性矩阵方法 状态空间与正则 子空间 

分 类 号：O151.21[理学—数学]