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Compound Product of Hypermatrices

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Abstract

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.

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Author information

Authors and Affiliations

  1. Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Daizhan Cheng, Xiao Zhang & Zhengping Ji

  2. Department of Control Science and Engineering, School of Electronics and Information Engineering, Tongji University, Shanghai, 201210, China

    Min Meng

  3. National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences, Beijing, 100190, China

    Xiao Zhang

  4. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100149, China

    Zhengping Ji

Authors
  1. Daizhan Cheng
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  2. Min Meng
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  3. Xiao Zhang
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  4. Zhengping Ji
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Corresponding author

Correspondence to Zhengping Ji.

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The authors declare no conflict of interest.

Additional information

This work was supported partly by the National Natural Science Foundation of China under Grant Nos. 62073315 and 62103305, Shanghai Pujiang Program under Grant No. 21PJ 1413100, and China Postdoctoral Science Foundation under Grant Nos. 2021M703423 and 2022T150686.

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Cite this article

Cheng, D., Meng, M., Zhang, X. et al. Compound Product of Hypermatrices. J Syst Sci Complex 37, 169–183 (2024). https://doi.org/10.1007/s11424-024-3331-9

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  • DOI: https://doi.org/10.1007/s11424-024-3331-9

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