幂零矩阵性质的再探讨  

Further Exploration of the Properties of Nilpotent Matrices

作　　者：高瑞 王蝶 GAO Rui;WANG Die(College of Mathematics,Cangzhou Normal University,Cangzhou,Hebei 061001,China;The Road Middle School,Suzhou,Anhui 234223,China)

机构地区：[1]沧州师范学院数学与统计学院,河北沧州061001 [2]安徽灵璧县大路中学,安徽宿州234223

出　　处：《沧州师范学院学报》2021年第1期90-92,118,共4页Journal of Cangzhou Normal University

摘　　要：通过对幂零矩阵的性质进行再探讨,得到了其转置矩阵、伴随矩阵等行列式也是零的结论,同时推广了k-幂零矩阵的性质,并对一些结论用不同的方法给予了证明.Through further exploration the properties of nilpotent matrix,it can be concluded that the determinant of transition matrix,adjoint matrix and etc.is zero.Meanwhile,the properties of k-nilpotent matrix were promoted.And some conclusions of k-nilpotent matrix were proved by different methods.

关 键 词：幂零矩阵 若尔当标准型 k-幂零矩阵 幂零线性变换 

分 类 号：O151.2[理学—基础数学]