This remarkable book develops the subject of linear algebra in a novel fashion. A logically interconnected sequence of propositions and problems--some 2,400 in all--appears 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...