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.
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页码：662 / 668
页数：7
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