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 hypermatri-ces with compatible orders and then extended to general cases.Three different types of hyperdetermi-nants 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.
Compound semi-tensor producthyperdeterminantshypereigenvalues and hypereigen-vectorshypergeneral linear groupshypermatrices
CHENG Daizhan、MENG Min、ZHANG Xiao、JI Zhengping
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Key Laboratory of Systems and Control,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China
Department of Control Science and Engineering,School of Electronics and Information Engineering,Tongji University,Shanghai 201210,China
National Center for Mathematics and Interdisciplinary Sciences,Chinese Academy of Sciences,Beijing 100190,China
School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100149,China
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