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
刊名	ADVANCES IN APPLIED CLIFFORD ALGEBRAS
	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
出版者	SPRINGER BASEL AG
WOS记录号	WOS:000396031500035
内容类型	期刊论文
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.