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Mathematical Modelling and Control

2021, Volume 1, Issue 1: 1-11. doi: 10.3934/mmc.2021001
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Research article

On numerical/non-numerical algebra: Semi-tensor product method

  • 1.
    Research Center of Semi-tensor Product of Matrices: Theory and Appllications, Liaocheng University, Liaocheng, China
  • 2.
    Key Laboratory of Systems and Control, AMSS, Chinese Academy of Sciences, Beijing, China
  • 3.
    School of Mathematics, Shandong University, Jinan 250100, Shandong, China
  • Received: 10 February 2021 Accepted: 13 March 2021 Published: 15 March 2021

  • A kind of algebra, called numerical algebra, is proposed and investigated. As its opponent, non-numerical algebra is also defined. The numeralization and dis-numeralization, which convert non-numerical algebra to numerical algebra and vise versa, are considered. Product structure matrix (PSM) of a finite dimensional algebra is constructed. Using PSM, some fundamental properties of finite dimensional algebras are obtained. Then a necessary and sufficient condition for a numerical algebra to be a field is presented. Finally, the invertibility of Segre (commutative) quaternion and some related properties of matrices over Segre quaternion are investigated.

    Citation: Daizhan Cheng, Ying Li, Jun-e Feng, Jianli Zhao. On numerical/non-numerical algebra: Semi-tensor product method[J]. Mathematical Modelling and Control, 2021, 1(1): 1-11. doi: 10.3934/mmc.2021001

    Related Papers:

  • A kind of algebra, called numerical algebra, is proposed and investigated. As its opponent, non-numerical algebra is also defined. The numeralization and dis-numeralization, which convert non-numerical algebra to numerical algebra and vise versa, are considered. Product structure matrix (PSM) of a finite dimensional algebra is constructed. Using PSM, some fundamental properties of finite dimensional algebras are obtained. Then a necessary and sufficient condition for a numerical algebra to be a field is presented. Finally, the invertibility of Segre (commutative) quaternion and some related properties of matrices over Segre quaternion are investigated.


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