Title: Local and global similarity of holomorphic matrices,
Abstract: R. Guralnick (Linear Algebra Appl. 99, 85-96, 1988) proved that two
holomorphic matrices on a noncompact connected Riemann surface, which are
locally holomorphically similar, are globally holomorphically similar. We
generalize this to (possibly, non-smooth) one-dimensional Stein spaces. For
Stein spaces of arbitrary dimension, we prove that global $\mathcal C^\infty$
similarity implies global holomorphic similarity, whereas global continuous
similarity is not sufficient.