两个二次矩阵线性组合的二次性  

Quadratic problems of linear combinations of two quadratic matrices

作　　者：谢涛[1] 刘慧娜[1] 余盛利[1] 

机构地区：[1]湖北师范学院数学与统计学院,湖北黄石435002

出　　处：《宝鸡文理学院学报（自然科学版）》2012年第2期16-20,共5页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：湖北省教育厅重点项目(D20122202);湖北省教育厅的青年项目(B20122203);湖北师范学院教研项目(XJ201107)

摘　　要：目的当P1,P2是2个满足方程(x-α)(x-β)=0的矩阵(称为二次矩阵),讨论了线性组合c1P1+c2P2仍是二次矩阵时系数(c1,c2)的完全分类。方法通过二次矩阵的性质和矩阵方程恒等式的性质。结果与结论将幂等矩阵、幂幺矩阵、幂零矩阵的线性组合的保持性问题推广到了二次矩阵的情形,概括了特殊矩阵线性组合性质的相关结果。Aim To discuss the complete classification of combination coefficients（c1,c2） such that linear combinations c1P1＋c2P2 is quadratic matrices when P1,P2 are two matrices satisfying the equation（which are called quadratic matrices）.Methods By using the properties of quadratic matrices and matrix equations,the aforesaid aim is investigated.Results and Conclusion The preserving problem of linear combinations of idempotent or involutary or nilpotent matrices is generalized to the case of quadratic matrices,which summarized the related results of properties of linear combinations of special matrices.

关 键 词：二次矩阵 幂等矩阵 幂零矩阵 对合矩阵 

分 类 号：O151.2[理学—数学]