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THE PROPERTIES OF A KIND OF RANDOM symplectic MATRICES

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Applied Mathematics and Mechanics(English Edition) 2002年第5期23卷 590-596页

作者： YAN Qing-you(闫庆友) Department of Applied Mathematics Dalian University of Technology Dalian 116024 P R China

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.

关键词： symplectic matrix QR-like algorithm eigenvalue condition number Jordan canonical form Schur canonical form

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Normal Forms of symplectic Matrices

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Acta Mathematica Sinica,English Series 2000年第2期16卷 237-260页

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 Nankai Institute of Mathematics Nankai University Tianjin 300071 P. R. China Department of Mathematics SUNY at Stony Brook Stony Brook NY 111794-3651 USA

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-1 MP is a symplectic matrix of the normal forms defined in this paper.

关键词： Normal form symplectic matrix Eigenvalue symplectic transformation

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New algorithms for constrained dynamics based on Faddeev-Jackiw approach

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Chinese Physics B 2007年第12期16卷 3581-3588页

作者：贾屹峰吴可许志强 School of Mathematical Sciences Capital Normal University Beijing 100037 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

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.

关键词： constrained characteristic chain symplectic matrix

Linear Operators Preserving symplectic Group over a Field Consisting of at Least Four Elements

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Northeastern Mathematical Journal 2006年第2期22卷 219-232页

作者：游宏刘绍武 Department of Mathematics Harbin Institute of Technology Harbin150001 Department of Mathematics Harbin Institute of Technology Harbin150001 School of Mathematical ScienceHeilongjiang UniversityHarbin150080

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.

关键词： linear preserver symplectic group symplectic matrix generalized symplectic matrix linear operator

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