多边矩阵的广义交叉乘法——处理复杂系统的新思维系列之二十四  

Generalized Cross Multiplies of Multilateral Matrix——New Thinking of Dealing with Complex Systems Series Twenty-four

作　　者：张应山[1] 张子晴[2] 罗纯[1,3] 

机构地区：[1]华东师范大学金融与统计学院,上海200241 [2]华东师范大学第二附属中学,上海201203 [3]上海应用技术学院理学院,上海201418

出　　处：《上海应用技术学院学报（自然科学版）》2014年第1期79-87,共9页Journal of Shanghai Institute of Technology: Natural Science

基　　金：上海市教委科研创新资助项目(14ZZ161)

摘　　要：本系列论文基于《多边矩阵理论》,由东方整体性思维所启迪,试图提供并完善一套从整体到局部处理复杂系统多指标问题、非均匀性问题、非线性问题的强有力的数学工具,并对其进行严格的理论推导和证明.作为系列论文的第24篇,介绍了多边矩阵的广义交叉乘法的概念,并给出了多种可以定义的运算,证明了这些运算满足结合律和分配律.作为应用,讨论了求最值运算的一些性质.This series of articles,based on'Multilateral Matrix Theory'and inspired by the Eastern holistic thinking,are trying to provide and improve a set of powerful mathematical tools to handle multi-target local issues,non-uniformity problems and nonlinear problems of complex system ranging from the whole to the part with rigorous theoretical analysis and proof.As the twenty-fourth paper of the series,the concept of the generalized cross multiplies of multilateral matrix was introduced,a variety of computing methods were presentd,and the conditions satisfying the associative law and the distributive law of these operations were proved.As an application,some properties of operations were discussed.

关 键 词：多边矩阵 广义交叉乘法 结合律 分配律 求最小值运算 

分 类 号：O151.21[理学—数学]