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		Daizhan CHENG,Zequn LIU.[en_title][J].Control Theory and Technology,2019,17(1):4~12.[Copy]

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A new semi-tensor product of matrices
DaizhanCHENG,ZequnLIU
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(The Key Laboratory of Systems and Control, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190, China)

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DOI：https://doi.org/10.1007/s11768-019-8161-2

基金项目:This work was supported in part by the National Natural Science Foundation of China (Nos. 61733018, 61333001, 61773371).

A new semi-tensor product of matrices

Daizhan CHENG,Zequn LIU

(The Key Laboratory of Systems and Control, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190, China;The Key Laboratory of Systems and Control, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China)

Abstract:

A new matrix product, called the second semi-tensor product (STP-II) of matrices is proposed. It is similar to the classical semi-tensor product (STP-I). First, its fundamental properties are presented. Then, the equivalence relation caused by STP-II is obtained. Using this equivalence, a quotient space is also obtained. Finally, the vector space structure, the metric and the metric topology, the projection and subspaces, etc. of the quotient space are investigated in detail.

Key words: Second sime-tensor product (STP-II), equivalence class, quotient space, topology, metric