Matrices of SL that are the Product of Two Skew-Symmetric Matrices
文献类型：期刊论文
| 作者 | Dong, Lei; Huang, Lei ; Shao, Changpeng; Wen, Yong
|
| 刊名 | ADVANCES IN APPLIED CLIFFORD ALGEBRAS
 |
| 出版日期 | 2017-03-01 |
| 卷号 | 27期号:1页码:475-489 |
| 关键词 | Oriented projective geometry Line geometry SL(4, R) Product of two skew-symmetric matrices SL(4, R)-Jordan form |
| ISSN号 | 0188-7009 |
| DOI | 10.1007/s00006-016-0701-y |
| 英文摘要 | The Jordan forms of matrices that are the product of two skew-symmetric matrices over a field of characteristic have been a research topic in linear algebra since the early twentieth century. For such a matrix, its Jordan form is not necessarily real, nor does the matrix similarity transformation change the matrix into the Jordan form. In 3-D oriented projective geometry, orientation-preserving projective transformations are matrices of , and those matrices of that are the product of two skew-symmetric matrices are the generators of the group . The canonical forms of orientation-preserving projective transformations under the group action of -similarity transformations, called -Jordan forms, are more useful in geometric applications than complex-valued Jordan forms. In this paper, we find all the -Jordan forms of the matrices of that are the product of two skew-symmetric matrices, and divide them into six classes, so that each class has an unambiguous geometric interpretation in 3-D oriented projective geometry. We then consider the lifts of these transformations to SO(3, 3) by extending the action of from points to lines in space, so that in the vector space spanned by the Plucker coordinates of lines these projective transformations become special orthogonal transformations, and the six classes are lifted to six different rotations in 2-D planes of . |
| 资助项目 | National High-tech R and D Program of China (863 Program)[2015AA011802] |
| WOS研究方向 | Mathematics ; Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000396031500035 |
| 出版者 | SPRINGER BASEL AG |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/24952]  |
| 专题 | 系统科学研究所 |
| 通讯作者 | Huang, Lei |
| 作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mech, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Dong, Lei,Huang, Lei,Shao, Changpeng,et al. Matrices of SL that are the Product of Two Skew-Symmetric Matrices[J]. ADVANCES IN APPLIED CLIFFORD ALGEBRAS,2017,27(1):475-489. |
| APA | Dong, Lei,Huang, Lei,Shao, Changpeng,&Wen, Yong.(2017).Matrices of SL that are the Product of Two Skew-Symmetric Matrices.ADVANCES IN APPLIED CLIFFORD ALGEBRAS,27(1),475-489. |
| MLA | Dong, Lei,et al."Matrices of SL that are the Product of Two Skew-Symmetric Matrices".ADVANCES IN APPLIED CLIFFORD ALGEBRAS 27.1(2017):475-489. |
入库方式： OAI收割
来源：数学与系统科学研究院
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