Ostrowski-Taussky不等式的推广

Extension of Ostrowski-Taussky Inequality

行列式的概念是矩阵分析中的一个很基本的概念,其中一个非常重要的应用就是解线性方程组.由于行列式的概念是和矩阵特征值紧密相关的,研究行列式的一些性质可以从侧面反映出该矩阵特征值的一些性质.Ostrowski-Taussky不等式是一个关于行列式的不等式,利用矩阵极分解的概念,给出了不等式的一个新的证明,并且推广了不等式.

The concept of determinant is a very basic concept in matrix analysis and a very important application is used in the linear equation group. Because the concept of determinant is closely related to the eigenvalues of matrices, some properties of eigenvalues can be studied from the determinant. Ostrowski-Taussky inequality is an inequality about determinant, and in this paper, we use the concept of polar decomposition of matrix to give a new proof of this inequality, and obtain one extension.