Compound Product of Hypermatrices
查看参考文献11篇
|
文摘
|
The semi-tensor product (STP) of matrices is generalized to multidimensional arrays, called the compound product of hypermatrices. The product is first defined for three-dimensional hypermatrices with compatible orders and then extended to general cases. Three different types of hyperdeterminants are introduced and certain properties are revealed. The Lie groups and Lie algebras corresponding to the hypermatrix products are constructed. Finally, these results are applied to dynamical systems. |
|
来源
|
Journal of Systems Science and Complexity
,2024,37(1):169-183 【核心库】
|
|
DOI
|
10.1007/s11424-024-3331-9
|
|
关键词
|
Compound semi-tensor product
;
hyperdeterminants
;
hypereigenvalues and hypereigenvectors
;
hypergeneral linear groups
;
hypermatrices
|
|
地址
|
1.
Academy of Mathematics and Systems Science,Chinese Academy of Sciences, Key Laboratory of Systems and Control,Chinese Academy of Sciences, Beijing, 100190
2.
Department of Control Science and Engineering,School of Electronics and Information Engineering,Tongji University, Shanghai, 201210
3.
National Center for Mathematics and Interdisciplinary Sciences,Chinese Academy of Sciences, Beijing, 100190
4.
School of Mathematical Sciences,University of Chinese Academy of Sciences, Beijing, 100149
|
|
语种
|
英文 |
|
文献类型
|
研究性论文 |
|
ISSN
|
1009-6124 |
|
学科
|
数学 |
|
基金
|
supported partly by the National Natural Science Foundation of China
;
上海市浦江人才计划项目
;
中国博士后科学基金
|
|
文献收藏号
|
CSCD:7659307
|
参考文献 共
11
共1页
|
|
1.
Cheng D.
Analysis and Control of Boolean Networks-A Semi-Tensor Product Approach,2011
|
CSCD被引
8
次
|
|
|
|
|
2.
Cheng D. A new semi-tensor product of matrices.
Control Theory and Technology,2019,17(1):14-22
|
CSCD被引
1
次
|
|
|
|
|
3.
Cheng D. On equivalence of matrices.
Asian Journal of Math,2019,23(2):257-348
|
CSCD被引
2
次
|
|
|
|
|
4.
Cheng D.
From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems,2019
|
CSCD被引
1
次
|
|
|
|
|
5.
Cheng D. From dimension-free manifolds to dimension-varying control systems.
Communications in Information and Systems,2023,23(1):85-150
|
CSCD被引
3
次
|
|
|
|
|
6.
Liu Z.
S-System Theory of Semigroup, 2nd Edition. (in Chinese),2008
|
CSCD被引
1
次
|
|
|
|
|
7.
Cheng D. Semi-tensor product of hypermatrices with application to compound hypermatrices.
arXiv: 2303.06295,2023
|
CSCD被引
1
次
|
|
|
|
|
8.
Cheng D. Contracted product of hypermatrices via STP of matrices.
Control Theory and Technology,2023
|
CSCD被引
1
次
|
|
|
|
|
9.
Lim L.
Tensors and hypermatrices, Handbook of Linear Algebra, 2nd Edition,2013
|
CSCD被引
1
次
|
|
|
|
|
10.
Hall B C.
Lie Algebras, and Representations-An Elementary Introduction,2003
|
CSCD被引
1
次
|
|
|
|
|
11.
Abraham R.
Foundations of Mechanics, 2nd Edition,1978
|
CSCD被引
1
次
|
|
|
|
|
了解气象卫星更多信息，请访问