四元数矩阵的Jordan标准形*
Jordan Canonical Forms of Matrices over Quaternion Field
-
摘要: 本文是在四元数矩阵的重行列式理论的基础上,直接利用四元数的乘法证明了。任意一个四元数矩阵都相似于特征主值表征的Jordan标准形及其唯一性。Abstract: Using quaternion multiplication and the double determinant theory over quaternion field. we proved that an arbitrary quaternion square matrix is similar to a unique Jordan canonical form indicated by its principal characteristic watues.
-
[1] 肖尚彬,四元数矩阵的乘法及其可易性,力学学报,(2) (1984), 159-166, [2] 张光枢,多刚体系统力学的四元数方法,北京航空学院科研报告,BH-B2361 (1986),24-31, [3] 王庆贵,四元数变换及其在空间机构位移分析中的应用,力学学报,(1) (1983), 54-61, [4] H, C, Lee, Eigenvalues and canonical forms of matrix with quaternion coefficients, Proc, R, I, A, SecA, 52(1949), 253-260, [5] L. X. Chen(陈龙玄),Inverse m atria and properties of double deter minant over quternion field,Science in China, Series A, 34(5) (1991), 528-540, [6] 陈龙玄,Cayley-Hamilton定理在四元数体上的推广,科学通报,36(17) (1991), 1291-1293, [7] 陈龙玄,四元数矩阵的特征值和特征向量,烟台大学学报,(自然科学与工程版).(3) (1993),1-8
计量
- 文章访问数: 2460
- HTML全文浏览量: 136
- PDF下载量: 699
- 被引次数: 0