快速判断一类实对称矩阵正定的极大极小元方法  

Max and mini-elements method: A rapid determination of one class rear symmetric positive definite matrices

作　　者：岑燕斌[1] 韦煜[1] 罗会亮[1] 

机构地区：[1]黔南民族师范学院数学系,贵州都匀558000

出　　处：《北京交通大学学报》2011年第6期140-143,146,共5页JOURNAL OF BEIJING JIAOTONG UNIVERSITY

基　　金：贵州省科技基金资助项目(20052004);黔南民族师范学院重点项目资助(2007Z05)

摘　　要：根据半正定矩阵的满秩分解,矩阵正定性的主对角线严格占优判别法,矩阵特征值估计的Gershgorin圆盘定理等矩阵论的相关理论,讨论了一类未必是主对角线严格占优的实对称矩阵的正定性,给出快速判断这一类实对称矩阵正定的极大极小元方法.We discuss the positive definition of one class on real symmetric matrices, in which every entry is not strictly main diagonal dominance, by full-rank decomposition, strictly main diagonal dominance rule and Gershgorin disk theorem, etc. Then a novel and simple method based on the maximal and minimal elements of the determined matrix for determining the positive definite matrices is proposed with rigorous proves.

关 键 词：实对称矩阵 正对角线严格占优 正元素 极大元 极小元 正定 

分 类 号：O151.21[理学—数学]