Higher Order Logarithmic Derivatives of Matrices in the Spectral Norm
Rajendra Bhatia, L. Elsner · SIAM Journal on Matrix Analysis and Applications · 2003
For the spectral norm $||.||$ on n × 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, $p=1,\infty$.