The derivative of a matric function
R. F. Rinehart · Proceedings of the American Mathematical Society · 1956
where A is a square matrix over the complex field and A is a scalar complex variable. This definition is not in keeping with the spirit of the definition of derivative of a scalar function of a complex variable, in that the mode of approach to zero by the incremental matrix is severely restricted, namely via scalar matrices only. It is natural to ask to what extent and under what circumstances a limit of the form of (1), with hi replaced by H, is independent of the mode of approach to zero of the incremental matrix H.