Canonical forms of holomorphic and meromorphic matrices

Canonical forms are powerful tools for spectral analysis of matrices. Smith form\index{Smith form} of a matrix polynomial and Smith-McMillan form\index{Smith-McMillan form} of a rational matrix are well known canonical forms which are used extensively in theory and applications. Although, local canonical forms such as local Smith form\index{Smith form}s of holomorphic and meromorphic matrices\index{meromorphic matrices} are well known in the literature, there has been relatively less research on global canonical forms of holomorphic and meromorphic matrices\index{meromorphic matrices}. Our aim is to fill this gap. We discuss, among other things, the global Smith form\index{Smith form} (resp., global Smith-McMillan form\index{Smith-McMillan form}) of a holomorphic (resp., meromorphic) matrix which is akin to the Smith form\index{Smith form} (resp., Smith-McMillan form\index{Smith-McMillan form}) of a matrix polynomial (resp., rational matrix).