These notes present a theorem on infinite matrices with values in a topological group due to P. Antosik and J. Mikusinski. Using the matrix theorem and classical gliding hump techniques, a number of applications to various topics in functional analysis, measure theory and sequence spaces are given. There are a number of generalizations of the classical Uniform Boundedness Principle given; in particular, using stronger notions of sequential convergence and boundedness due to Antosik and Mikusinki, versions of the Uniform Boundedness Principle and the Banach-Steinhaus Theorem are given which,...