Some theorems on holomorphic matrices

We consider holomorphic m x m-matrices, i.e. m x m-matrices whose matrix elements are holomorphic functions on a connected open set G in the space C_n of n complex variables.After giving some physical motivation for this research we discuss the analytic behavior of the eigenvalues, the construction of a G-adherent transformation matrix and a (physically) useful commutator theory. Vorgelegt von H. Görtler