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 Mikusinski, versions of the Uniform Boundedness Principle and the Banach-Steinhaus Theorem are given which, in contrast to the usual versions, require no completeness or barrelledness assumptions on the domain space. Versions of Nikodym Boundedness and Convergence Theorems of measure theory, the Orlicz-Pettis Theorem on subseries convergence, generalizations of the Schur Lemma on the equivalence of weak and norm convergence in l1 and the Mazur-Orlicz Theorem on the continuity of separately continuous bilinear mappings are also given. Finally, the matrix theorems are also employed to treat a number of topics in sequence spaces.Contents:IntroductionThe Antosik-Mikusinski Matrix Theoremk-Convergence and k-BoundednessThe Uniform Boundedness PrincipleThe Banach-Steinhaus TheoremContinuity and Hypocontinuity for Bilinear MapsPap's Adjoint TheoremVector Versions of the Hahn-Schur TheoremsAn Abstract Hahn-Schur TheoremThe Orlicz-Pettis TheoremImbedding c0 and l∞Sequence SpacesReadership: Graduate students in pure mathematics.Key Features:Information is rapidly accessible. Uses bulleted lists format (as opposed to dense textbook paragraphs) and easy to read tables to allow for quick review in real time (while the clinician is with their patient)Interspersed multiple choice questions will enable readers to test their knowledge as they progress through the handbook. These questions, stylized after standard board questions, will thereby serve clinicians in real time while delivering patient care, but also serve as board-review material as students/clinicians prepare for in-service or board examinations for school or licensureRather than a rapidly aging bibliography, the volume provides a wide array of responsible web resources for the clinician to access