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Linear Operators Preserving Symplectic Group over a Field Consisting of at Least Four Elements
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作者 游宏 刘绍武 《Northeastern Mathematical Journal》 CSCD 2006年第2期219-232,共14页
Suppose F is a field consisting of at least four elements. Let Mn(F) and SP2n(F) be the linear space of all n × n matrices and the group of all 2n × 2n symplectic matrices over F, respectively. A linear ... Suppose F is a field consisting of at least four elements. Let Mn(F) and SP2n(F) be the linear space of all n × n matrices and the group of all 2n × 2n symplectic matrices over F, respectively. A linear operator L : M2n(F) → M2n(F) is said to preserve the symplectic group if L(SP2n(F)) = SP2n(F). It is shown that L is an invertible preserver of the symplectic group if and only if L takes the form (i) L(X) = QPXP^-1 for any X ∈ M2n(F) or (ii) L(X) = QPX^TP^-1 for any X ∈M2n(F), where Q ∈ SP2n(F) and P is a generalized symplectic matrix. This generalizes the result derived by Pierce in Canad J. Math., 3(1975), 715-724. 展开更多
关键词 linear preserver symplectic group symplectic matrix generalized symplectic matrix linear operator
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THE PROPERTIES OF A KIND OF RANDOM SYMPLECTIC MATRICES
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作者 YAN Qing-you(闫庆友) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第5期590-596,共7页
Several important properties of a kind of random symplectic matrix used by A. Bunse-Gerstner and V. Mehrmann are studied and the following results are obtained: 1) It can be transformed to Jordan canonical form by ort... Several important properties of a kind of random symplectic matrix used by A. Bunse-Gerstner and V. Mehrmann are studied and the following results are obtained: 1) It can be transformed to Jordan canonical form by orthogonal similar transformation; 2) Its condition number is a constant; 3) The condition number of it is about 2.618. 展开更多
关键词 symplectic matrix QR-like algorithm EIGENVALUE condition number Jordan canonical form Schur canonical form
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High order symplectic conservative perturbation method for time-varying Hamiltonian system 被引量:1
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作者 Ming-Hui Fu Ke-Lang Lu Lin-Hua Lan 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2012年第3期885-890,共6页
This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order... This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order pertur- bation equation, which is solved approximately by resolv- ing the Hamiltonian coefficient matrix into a "major compo- nent" and a "high order small quantity" and using perturba- tion transformation technique, then the solution to the orig- inal equation of Hamiltonian system is determined through a series of inverse transform. Because the transfer matrix determined by the method in this paper is the product of a series of exponential matrixes, the transfer matrix is a sym- plectic matrix; furthermore, the exponential matrices can be calculated accurately by the precise time integration method, so the method presented in this paper has fine accuracy, ef- ficiency and stability. The examples show that the proposed method can also give good results even though a large time step is selected, and with the increase of the perturbation or- der, the perturbation solutions tend to exact solutions rapidly. 展开更多
关键词 Time-varying Hamiltonian system High ordermultiplicative perturbation symplectic conservation expo-nential matrix Precise time integration method
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New algorithms for constrained dynamics based on Faddeev-Jackiw approach
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作者 贾屹峰 吴可 许志强 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第12期3581-3588,共8页
In this paper, the Faddeev Jackiw approach is improved by the Wu elimination method, so a great many complicated computations in solving constraints for the finite-dimensional polynomial-type constrained dynamics can ... In this paper, the Faddeev Jackiw approach is improved by the Wu elimination method, so a great many complicated computations in solving constraints for the finite-dimensional polynomial-type constrained dynamics can be executed easily by using computers. Moreover, based on the Faddeev Jackiw approach, a new algorithm of solving the constrained dynamics is presented. The new algorithm is simpler and stricter than the Faddeev-Jackiw approach. Using the new algorithm, the second Cawley counterexample is solved. 展开更多
关键词 CONSTRAINED characteristic chain symplectic matrix
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Normal Forms of Symplectic Matrices 被引量:2
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作者 Yiming Long Nankai Institute of Mathematics.Nankai University,Tianjin 300071,P.R.China Di Dong Department of Mathematics.SUNY at Stony Brook,Stony Brook,NY 111794-3651,USA Associate Member of the ICTP 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2000年第2期237-260,共24页
In this paper,we prove that for every symplectic matrix M possessing eigenvalues on the unit circle,there exists a symplectic matrix P such that P<sup>-1</sup> MP is a symplectic matrix of the normal forms... In this paper,we prove that for every symplectic matrix M possessing eigenvalues on the unit circle,there exists a symplectic matrix P such that P<sup>-1</sup> MP is a symplectic matrix of the normal forms defined in this paper. 展开更多
关键词 Normal form symplectic matrix EIGENVALUE symplectic transformation
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