A Systematic Presentation in Problem Form - I. M. Glazman; Ju. I. Ljubic (New York, 2006)
This remarkable book develops the subject of linear algebra in a novel fashion. A logically interconnected sequence of propositions and problemssome 2,400 in allappears without proofs. Assisted only by hints and pointers, students must work out formal proofs systematically, proceeding from simple verifications to relatively advanced strategies and techniques of proof.This volume also presents insights into functional analysis, which may be formulated as linear analysis without an infinite dimensional framework. As students allow their consideration of the propositions to move toward the limiting case of unrestricted dimensionality, they will find that their conceptual outlook approaches that which is suitable to functional analysis. In this regard, the book represents an introduction to the latter subject, free of the difficulties inherent in the explicit admission of infinities.
English
Keywords: Finite-Dimensional; Linear alegbra; Linear Analysis