Higher order logarithmic derivatives of matrices in the spectral norm
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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