实数域上的次辛矩阵  

Sub-Symplectic Matrix in Real Field

作　　者：刘玉[1] 许滋燕[1] 

机构地区：[1]韩山师范学院数学与信息技术系,广东潮州521041

出　　处：《中北大学学报（自然科学版）》2011年第5期534-539,共6页Journal of North University of China(Natural Science Edition)

基　　金：广东省自然科学基金资助项目(10152104101000008)

摘　　要：将辛矩阵定义中所采用的转置矩阵改其为实次转置矩阵,得出了实数域上次辛矩阵的概念,利用次转置矩阵的性质推导出了实次辛矩阵的转置、次转置、逆、伴随及行列式等的基本性质,讨论了实次辛矩阵与次正交、次对称等特殊矩阵之间的关系,研究了实次辛矩阵的特征值问题,得到了一个新的群——实次辛矩阵群以及其它一些与实次辛矩阵相关的新结果.By replacing the transposed matrix to a real sub-transposed matrix in the definitional expression of symplectic matrix,the concept of real sub-symplectic matrix was proposed.By using the properties of sub-transposed matrix,the properties of transposed matrix,sub-transpose matrix,inverse matrix,adjoint and determinant of real sub-transposed matrix were deduced.Relations between real sub-symplectic matrix and some special matrices,such as sub-symmetric matrix,sub-orthogonal matrix and so on,were discussed.The eigenvalue problem of real sub-transposed matrix was investigated.Real sub-transposed matrix group was proposed and other relevant solutions were obtained.

关 键 词：实数域 辛矩阵 次辛矩阵 特征值 

分 类 号：O151.21[理学—数学]