Matrices of SL that are the Product of Two Skew-Symmetric Matrices

doi:10.1007/s00006-016-0701-y

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	Matrices of SL that are the Product of Two Skew-Symmetric Matrices
	Dong, Lei; Huang, Lei; Shao, Changpeng; Wen, Yong
	2017-03-01
发表期刊	ADVANCES IN APPLIED CLIFFORD ALGEBRAS
ISSN	0188-7009
卷号	27 期号:1 页码:475-489
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 .
关键词	Oriented projective geometry Line geometry SL(4, R) Product of two skew-symmetric matrices SL(4, R)-Jordan form
DOI	10.1007/s00006-016-0701-y
语种	英语
资助项目	National High-tech R and D Program of China (863 Program)[2015AA011802]
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Mathematical
WOS记录号	WOS:000396031500035
出版者	SPRINGER BASEL AG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/24953
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.