Higher order logarithmic derivatives of matrices in the spectral norm

被引：6

作者：

Bhatia, R ^{[1
]}

Elsner, L

机构：

[1] Indian Stat Inst, New Delhi 110016, India

[2] Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2003年 / 25卷 / 03期

关键词：

logarithmic derivative; exponential function; higher order derivatives;

D O I：

10.1137/S0895479802413662

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For the spectral norm ||.|| on n x n complex matrices, we derive the first three right-hand derivatives of phi(t) = ||e(tA)|| at t = 0. The first one is the well-known logarithmic derivative. This study was inspired by a recent result by Kohaupt, where the second derivative is studied for the l(p) norms, p = 1,infinity.

引用

页码：662 / 668

页数：7

共 6 条

[1]

DAHLQUIST G, 1959, KUNGL TEKN HOGSK HAN, V130

[2] SENSITIVITY ANALYSIS OF ALL EIGENVALUES OF A SYMMETRICAL MATRIX [J].