| 立体阵的一般结构 |
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| 引用本文： | 张利军,程代展,李春文.立体阵的一般结构[J].系统科学与数学,2005,25(4):439-450. |
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| 作者姓名： | 张利军 程代展 李春文 |
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| 作者单位： | 1. 清华大学自动化系控制理论与技术研究所,北京,100084
2. 中国科学院数学与系统科学研究院系统科学研究所,北京,100080 |
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| 基金项目： | 国家自然科学基金(G59837270，60274025，60343001)
博士后基金(2004036105) |
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| 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。
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| 关 键 词： | 立体阵 矩阵的半张量积 高维矩阵 纳什均衡 |
| 修稿时间： | 2003年1月3日 |
THE GENERAL STRUCTURE OF CUBIC MATRICES |
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| Zhang Lijun,Cheng Daizhan,Li Chunwen.THE GENERAL STRUCTURE OF CUBIC MATRICES[J].Journal of Systems Science and Mathematical Sciences,2005,25(4):439-450. |
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| Authors: | Zhang Lijun Cheng Daizhan Li Chunwen |
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| Institution: | (1)Department of Automation, Tsinghua University, Beijing 100084;(2)Institute of Systems Science, Chinese Academy of Sciences, Beijing, 100080;(3)Department of Automation, Tsinghua University, Beijing 100084 |
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| Abstract: | 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. |
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| Keywords: | Cubic matrix semi-tensor product of matrices multi-demensional matrix Nash equilibrium |
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