二、三阶方阵的等迹分解  

The equal trace decompositions of second order and third order square matrices

作　　者：吴马威 陈益智[2] 骆莉芳 

机构地区：[1]广西大学数学与信息科学学院,广西南宁530004 [2]惠州学院数学系,广东惠州516007

出　　处：《纺织高校基础科学学报》2017年第1期1-5,共5页Basic Sciences Journal of Textile Universities

基　　金：广东省自然科学基金资助项目(2015A030310119);广东省高校优秀青年教师培养计划项目(YQ2015155);广东大学生科技创新培育专项资金项目(PDJH2016B0477)

摘　　要：利用构造法探究二、三阶方阵的等迹分解.首先证明任意二阶方阵都存在等迹分解;然后证明对角线元素均不为零且对角线元素互不相等的三阶方阵可以分解为迹为1的两个方阵相乘,如果该方阵还满足迹不为零的条件,则该方阵存在等迹分解,并证明了一类特殊三阶块对角阵也存在等迹分解.最后通过数值算例给出了主要结果的一个应用.The equal trace decompositions of second and third order square matrices are mainly studied by using construction methods.Firstly,it is proved that the equal trace decompositions exists if the matrix is second order square matrix;and then some third order square matrices satisfying that any diagonal entry is different from each other and nonzero,can be decomposed into two matrices with trace-1;Moreover,it is showed that the equal trace decompositions exists if the traces of these matrices is nonzero,and the equal trace decompositions of some kind of third-order block diagonal matrices also exist.Finally,one application of the main results is given by an example.

关 键 词：二阶方阵 三阶方阵 等迹分解 

分 类 号：O152.7[理学—数学]