摘要
本文给出了立体阵的各种表示形式及立体阵乘法的各种定义,推导出其主要性质,说明立体阵的乘积在适当情况下可转化成普通矩阵乘积。然后讨论了立体阵的乘积与矩阵半张量积的关系,并用矩阵半张量积统一了各种立体阵的乘法运算。最后以对策论为例说明它的应用。
In this paper, all kinds of expressions and various definitions of products of cubic matrices are presented. Their properties are investigated. Consequently, we show that all products of cubic matrices can be converted into products of general matrices under certain appropriate conditions. Then the relationship between semi-tensor product of matrices and product of cubic matrices is studied. The semi-tensor product of matrices is used to unify the various products of cubic matrices. An example in game theory is implemented to illustrate the applications.
出处
《系统科学与数学》
CSCD
北大核心
2005年第4期439-450,共12页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(G59837270
60274025
60343001)博士后基金(2004036105)
