Basis-free solution to general linear quaternionic equation
文献类型：期刊论文
| 作者 | Shao, Changpeng; Li, Hongbo1,2; Huang, Lei |
| 刊名 | LINEAR & MULTILINEAR ALGEBRA
 |
| 出版日期 | 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 |
| WOS记录号 | WOS:000587891600002 |
| 出版者 | TAYLOR & FRANCIS LTD |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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