Basis-free solution to general linear quaternionic equation

doi:10.1080/03081087.2018.1508404

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	Basis-free solution to general linear quaternionic equation
	Shao, Changpeng ; Li, Hongbo 1,2; Huang, Lei
	2020-03-03
发表期刊	LINEAR & MULTILINEAR ALGEBRA
ISSN	0308-1087
卷号	68 期号:3 页码:435-457
摘要	A linear quaternionic equation in one quaternionic variable q is of the form a1qb1+a2qb2+MIDLINE HORIZONTAL ELLIPSIS+amqbm=c, where the ai,bj,c are given quaternionic coefficients. If introducing basis elements i,j,k of pure quaternions, then the quaternionic equation becomes four linear equations in four unknowns over the reals, and solving such equations is trivial. On the other hand, finding a quaternionic rational function expression of the solution that involves only the input quaternionic coefficients and their conjugates, called a basis-free solution, is non-trivial. In 1884, Sylvester initiated the study of basis-free solution to linear quaternionic equation. He considered the three-termed equation aq+qb=c, and found its solution q=(a2+bb over bar +a(b+b over bar ))-1(ac+cb over bar ) by successive left and right multiplications. In 2013, Schwartz extended the technique to the four-termed equation, and obtained the basis-free solution in explicit form. This paper solves the general problem for arbitrary number of terms in the non-degenerate case.
关键词	Linear quaternionic equation Sylvester equation basis-free solution clifford algebra Primary Secondary
DOI	10.1080/03081087.2018.1508404
收录类别	SCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000587891600002
出版者	TAYLOR & FRANCIS LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52425
专题	中国科学院数学与系统科学研究院
通讯作者	Li, Hongbo
作者单位	1.Chinese Acad Sci, KLMM, AMSS, Beijing 100190, Peoples R China 2.Chinese Acad Sci, UCAS, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Shao, Changpeng,Li, Hongbo,Huang, Lei. Basis-free solution to general linear quaternionic equation[J]. LINEAR & MULTILINEAR ALGEBRA,2020,68(3):435-457.
APA	Shao, Changpeng,Li, Hongbo,&Huang, Lei.(2020).Basis-free solution to general linear quaternionic equation.LINEAR & MULTILINEAR ALGEBRA,68(3),435-457.
MLA	Shao, Changpeng,et al."Basis-free solution to general linear quaternionic equation".LINEAR & MULTILINEAR ALGEBRA 68.3(2020):435-457.