2个矩阵行列式之差上界的新估计

设A,E为n×n阶矩阵,对于2个矩阵行列式之差的上界估计,有结论 det(A+E)-det(A)≤∑n i=1(n i) An-i2Ei2≤(A2+E2)n-An2.其中这里的A2表示矩阵A的谱范数.通过一种新的矩阵范数改进该结论,运用Matlab进行了实例验证,结果更优.

关于实四元数方阵数值半径的注记

文[1]给出了实四元数方阵数值半径的概念和一些不等式。文[2]给出了数值半径幂的不等式，C—数值半径所满足的不等式。本文在[1]与[2]的基础上研究了数值半径，矩阵的谱范数和矩阵范数之间的关系，又给出了一些新的不等式。有些不等式在复矩阵理论中也是新的。

On the p-norm joint spectral radius

The p-norm joint spectral radius is defined by a bounded collection of square matrices with complex entries and of the same size. In the present paper the author investigates the p-norm joint spectral radius for integers. The method introduced in this paper yields some basic formulas for these spectral radii. The approach used in this paper provides a simple proof of Berger-Wang' s relation concerning the ∞-norm joint spectral radius.