用矩阵的迹与行列式估计矩阵的奇异值  

Estimating the Bounds of Singular Values Using the Trace and Determinant of Matrices

作　　者：张吉林[1] 

机构地区：[1]塔里木大学文理学院,新疆阿拉尔843300

出　　处：《塔里木大学学报》2008年第1期34-35,87,共3页Journal of Tarim University

摘　　要：本文给出非奇异矩阵A的奇异值的从大到小的排列,利用代数-几何均值不等式以及矩阵奇异值的性质,得到矩阵奇异值和与积的一些不等式,而这些不等式仅仅用到k,l,n矩阵的迹与行列式。最后我们用一些具体的例子来说明这些不等式的优越性。In this paper, the singular value of nonsingular matrix A is ordered, By the use of the arithmetic - geometric mean inequality and the properties of singular value of matrices, We obtain some inequalities of sum and product of the singular value. These inequalities only involve k,l,n trace and determinant of the matrices. Finally, we give some examples to show the effectiveness of the new inequalities.

关 键 词：非奇异矩阵 矩阵的迹 行列式 奇异值 

分 类 号：O151.21[理学—数学]