KMS Of Academy of mathematics and systems sciences, CAS
Generalised semi-tensor product of matrices | |
Cheng, Daizhan1; Liu, Zequn1,2; Xu, Zhenhui3; Shen, Tielong3 | |
2020 | |
发表期刊 | IET CONTROL THEORY AND APPLICATIONS |
ISSN | 1751-8644 |
卷号 | 14期号:1页码:85-95 |
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. |
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 |
DOI | 10.1049/iet-cta.2019.0337 |
收录类别 | SCI |
语种 | 英语 |
WOS研究方向 | Automation & Control Systems ; Engineering ; Instruments & Instrumentation |
WOS类目 | Automation & Control Systems ; Engineering, Electrical & Electronic ; Instruments & Instrumentation |
WOS记录号 | WOS:000505200300009 |
出版者 | INST ENGINEERING TECHNOLOGY-IET |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/50437 |
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.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Sophia Univ, Dept Mech, Tokyo, Japan |
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. |
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