ON THE RECIPROCAL THEOREM AND ADJOINT SIMPLETIC ORTHOGONAL RELATION
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摘要: 本文指出,哈密尔顿矩阵的本征向量间的辛正交关系可以由结构力学的互等性定理导出。尤其当哈密尔顿矩阵出现多重本征根以及约当(Jordan)型时,本文指出了使约当型保持哈密尔顿矩阵结构形式不变的变换;并且证明了对于次本征向量的恰当选择可以使各个(次)本征向量之间仍保持共轭辛正交归一关系。Abstract: The paper indicates that the simpletic orthogonal relation among eigenvectors of a Hamiltonian matrix can be derived by the reciprocal theorem of structural mechanics. It also presents the transformation which makes a Jordan-type matrix preserve the structure of a Hamiltonian matrix and proves that suitable arrangement of secondary eigenvectors keeps simpletic orthogonality among them.
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Key words:
- reciprocal theorem /
- hamiltonian matrix /
- eigen-problem/sirnpletic
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