ON EQUIVALENCE OF MATRICES
文献类型：期刊论文
| 作者 | Cheng, Daizhan
|
| 刊名 | ASIAN JOURNAL OF MATHEMATICS
 |
| 出版日期 | 2019-04-01 |
| 卷号 | 23期号:2页码:257-347 |
| 关键词 | Semi-tensor product/addition(STP/STA) vector product/addition(VP/VA) matrix/vector equivalence (M-/V-) lattice topology fiber bundle bundled manifold/Lie algebra/Lie group(BM/BLA/BLG) |
| ISSN号 | 1093-6106 |
| 英文摘要 | A new matrix product, called the semi-tensor product (STP), is briefly reviewed. The STP extends the classical matrix product to two arbitrary matrices. Under STP the set of matrices becomes a monoid (semi-group with identity). Some related structures and properties are investigated. Then the generalized matrix addition is also introduced, which extends the classical matrix addition to a class of two matrices with different dimensions. Motivated by STP of matrices, two kinds of equivalences of matrices (including vectors) are introduced, which are called matrix equivalence (M-equivalence) and vector equivalence (V-equivalence) respectively. The lattice structure has been established for each equivalence. Under each equivalence, the corresponding quotient space becomes a vector space. Under M-equivalence, many algebraic, geometric, and analytic structures have been posed to the quotient space, which include (i) lattice structure; (ii) inner product and norm (distance); (iii) topology; (iv) a fiber bundle structure, called the discrete bundle; (v) bundled differential manifold; (vi) bundled Lie group and Lie algebra. Under V-equivalence, vectors of different dimensions form a vector space V, and a matrix A of arbitrary dimension is considered as an operator (linear mapping) on V. When A is a bounded operator (not necessarily square but includes square matrices as a special case), the generalized characteristic function. eigenvalue and eigenvector etc. are defined. In one word, this new matrix theory overcomes the dimensional barrier in certain sense. It provides much more freedom for using matrix approach to practical problems. |
| 资助项目 | National Natural Science Foundation of China[61773371] ; National Natural Science Foundation of China[61733018] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000473276100003 |
| 出版者 | INT PRESS BOSTON, INC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/35187]  |
| 专题 | 系统科学研究所 |
| 通讯作者 | Cheng, Daizhan |
| 作者单位 | Chinese Acad Sci, AMSS, Key Lab Syst & Control, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Cheng, Daizhan. ON EQUIVALENCE OF MATRICES[J]. ASIAN JOURNAL OF MATHEMATICS,2019,23(2):257-347. |
| APA | Cheng, Daizhan.(2019).ON EQUIVALENCE OF MATRICES.ASIAN JOURNAL OF MATHEMATICS,23(2),257-347. |
| MLA | Cheng, Daizhan."ON EQUIVALENCE OF MATRICES".ASIAN JOURNAL OF MATHEMATICS 23.2(2019):257-347. |
入库方式： OAI收割
来源：数学与系统科学研究院
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