Generalized Diagonalization of Matrices Over Quaternion Field
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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。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.
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Key words:
- complex quaternion ring /
- quaternion field /
- matrix /
- diagonalization matrix
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[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.
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