Generalised semi-tensor product of matrices

doi:10.1049/iet-cta.2019.0337

	Generalised semi-tensor product of matrices
	Cheng, Daizhan 1; Liu, Zequn 1,3; Xu, Zhenhui 2; Shen, Tielong 2
刊名	IET CONTROL THEORY AND APPLICATIONS
	2020
卷号	14 期号:1 页码:85-95
关键词	vectors tensors matrix algebra group theory linear S-system dynamic linear system matrix multiplier vector multiplier two kinds matrix-vector STPs standard STP consistent MM-STP MV-STP cross-dimensional linear system linear semigroup system quotient matrix space quotient vector space S-system structure quotient vector spaces inner-product cross-dimensional state space matrix-matrix STPs generalised semitensor product
ISSN号	1751-8644
DOI	10.1049/iet-cta.2019.0337
英文摘要	By introducing matrix multiplier and vector multiplier two kinds of semi-tensor products (STPs), called matrix-matrix (MM) STPs and matrix-vector (MV) STPs, are introduced. They are generalisations of conventional matrix product, and contain standard STP as a particular case. Certain properties are revealed. Using consistent MM-STP and MV-STP, a cross-dimensional linear system is proposed. It is shown that the cross-dimensional linear system is a linear semi-group (S) system. Next, the quotient matrix space based on matrix multiplier and the quotient vector space based on vector multiplier are introduced, and the S-system structure is extended to quotient matrix and quotient vector spaces. Finally, an inner-product is introduced, which poses a topology on the cross-dimensional state space and hence turns the linear S-system into a dynamic linear system.
WOS研究方向	Automation & Control Systems ; Engineering ; Instruments & Instrumentation
语种	英语
出版者	INST ENGINEERING TECHNOLOGY-IET
WOS记录号	WOS:000505200300009
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/50436]
专题	中国科学院数学与系统科学研究院
通讯作者	Cheng, Daizhan
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 2.Sophia Univ, Dept Mech, Tokyo, Japan 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Cheng, Daizhan,Liu, Zequn,Xu, Zhenhui,et al. Generalised semi-tensor product of matrices[J]. IET CONTROL THEORY AND APPLICATIONS,2020,14(1):85-95.
APA	Cheng, Daizhan,Liu, Zequn,Xu, Zhenhui,&Shen, Tielong.(2020).Generalised semi-tensor product of matrices.IET CONTROL THEORY AND APPLICATIONS,14(1),85-95.
MLA	Cheng, Daizhan,et al."Generalised semi-tensor product of matrices".IET CONTROL THEORY AND APPLICATIONS 14.1(2020):85-95.