Conditioning and Pade approximation of the logarithm of a matrix

In this work we (i) use the theory of piecewise analytic functions to repre sent the Frechet derivative of any primary matrix function, in particular o f primary logarithms; (ii) propose an indicator to assess inherent difficul ties to compute a logarithm; and (iii) revisit Pade approximation technique s for the principal logarithm of block triangular matrices.