Spectral characterization of the Jordan form

Denote by M-n(C) the set of complex n x n matrices, and let A is an element of M-n(C). We give a variational, purely spectral characterization of the Jordan form of A by examining the characteristic polynomial of the perturbe d matrices tA + X for t is an element of C and X is an element of M-n(C). T his allows us to give a more elementary proof of a theorem of Baribeau and Ransford on spectrum-presenting holomorphic maps on M-n(C). (C) 2000 Elsevi er Science Inc. Ail rights reserved. AMS Classification: 15A21; 15A18.