The Double Determinant of Vandermonde’s Type Over Quaternion Field
-
摘要: 讨论了四元数体上的Vandermonde重行列式问题,给出了Vandermonde重行列式不为零的充分必要条件.
-
关键词:
- 四元数体 /
- 重行列式 /
- Vandermonde行列式
Abstract: Based on the double determinant theory the problem about the determinant of Vandermonde's type over quaternion field is studied,and a necessary and sufficient condition that this double determinant is not equal to zero is got.-
Key words:
- quaternion field /
- double determinant /
- Vandermonde determinant
-
[1] Winograd S.On computingthe discrete Fourier transform[J].Proc Nat Acad Sci U S A,1976,73(1):42~46. [2] Wang Shasheng,Tu Fengsheng.Extension of Vandermonde determinant and itsapplications to theory of control[J].Acta Mathematica Scientia,1984,4(3):329~337. [3] Jin Zhaoyong.Vandermonde matrix and decentralized stabilization forlarge scale systems[J].Applied Mathematics a Journalof Chinese Universities(Ser A),1997,12(2):219~227.(in Chinese) [4] Davis P J.Circulant Matrices[M].New York:Wiley,1979. [5] 肖尚彬.四元数矩阵的乘法及其可易性[J].力学学报,1984,16(2):159~166. [6] 张光枢.多刚体系统力学的四元数方法[R].北京航空学院科研报告.BH-B 2361,1986,24~31. [7] 王庆贵.四元数变换及其在空间机构位移分析中的应用[J].力学学报,1983,15(1):54~61. [8] Chen Longxuan.Definition of determinantand cramer solution over quaternion field[J].Acta Math Sinica New Series,1991,7(2):171~180. [9] Chen Longxuan.Inverse matrix and properties ofdouble determinant over quaternion field[J].Sciencein China(Series A),1991,34(5):528~540. [10] 侯仁民.四元数体上重行列式与逆矩阵的计算[J].烟台大学学报(自然科学与工程版),1994,7(4):5~9. [11] 吴光磊,丁石孙.解析几何[M].北京:人民教育出版社,1978,60~61.
计量
- 文章访问数: 2921
- HTML全文浏览量: 131
- PDF下载量: 703
- 被引次数: 0