Basis-free solution to general linear quaternionic equation

doi:10.1080/03081087.2018.1508404

	Basis-free solution to general linear quaternionic equation
	Shao, Changpeng ; Li, Hongbo 1,2; Huang, Lei
刊名	LINEAR & MULTILINEAR ALGEBRA
	2020-03-03
卷号	68 期号:3 页码:435-457
关键词	Linear quaternionic equation Sylvester equation basis-free solution clifford algebra Primary Secondary
ISSN号	0308-1087
DOI	10.1080/03081087.2018.1508404
英文摘要	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.
WOS研究方向	Mathematics
语种	英语
出版者	TAYLOR & FRANCIS LTD
WOS记录号	WOS:000587891600002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/52424]
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.