四元数体上矩阵的广义对角化

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基金项目: 山东省自然科学基金

Generalized Diagonalization of Matrices Over Quaternion Field

1.
Department of Mathematics, Linyi Teachers College, Linyi, Shandong 276005, P R China;
2.
Department of Physics, Linyi Teachers College, Linyi, Shandong 276005, P R China

摘要: 引入了复四元数环和四元数体上矩阵可对角化的概念,研究了复四元数环上矩阵的性质,给出了四元数体上矩阵可对角化的充分必要条件和求矩阵对角化的方法。
- 复四元数环 /
- 四元数体 /
- 矩阵 /
- 对角化矩阵
Abstract: A concept of diagonalization matrix over quaternion field is given, the necessary and sufficient conditions for determining whether a quaternion matrix is a diagonalization one are discussed, and a method of diagonalization of matrices over quaternion field is given.
- complex quaternion ring /
- quaternion field /
- matrix /
- diagonalization matrix

[1]	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.
[2]	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.
[3]	Adler S L.Quaternionic Quantum Mechanics and Quantum Fields[M].New York:Oxford U P,1994.
[4]	陈龙玄,侯仁民,王亮涛.四元数矩阵的Jordan标准形[J].应用数学和力学,1996,17(6):533～541.
[5]	Nathan Jacobson.Basic Algebra,I[M].San Francisco:W H Freeman and Company,1974,95～97.
[6]	Zhang Fuzhen.Quaternions and matrices of quaternions[J].Linear Algebra Appl,1997,251:21～57.
[7]	Birkhoff G,Saunders M L.A Survey of Modern Algebra[M].Fourth edition,New York:Macmillan Publishing Co,Inc,1977,150～151.
[8]	Stuart J L,Weaver J R.Matrices that commute with a permutation matrix[J].Linear Algebra Appl,1991,150:255～265.
[9]	Larry Smith.Linear Algebra[M].New York:Springer-Verlag,1978,208.
[10]	Kenneth Hoffmna,Kunze Ray.Linear Algebra[M].Second Edition.Englewood Cliffs,New Jersey:Prentice-Hall,Inc,1991,244～246.