Linear Algebra Uncluttered

Linear algebra is the study of vector spaces and linear maps, and this study provides many foundations for other branches of mathematics which rely on it. This book, based upon over a decade of independent study outside the classroom, is a detailed and thorough introduction to the subject. The work begins with the preliminary definitions and facts of vector spaces and linear maps and then develops these in tandem. Unlike other books on the subject, this book is not filled with pages and pages of examples and exercises drilling the reader in overactive practice and distracting from the underlying concepts. Throughout the development, the topics are presented with an emphasis on theory over application. The reader is assumed to have no previous knowledge of linear algebra, although some experience with logic as used in mathematical proofs such as induction and contraposition will be helpful. A good understanding of sets and maps will also be helpful. The book is not intended as a textbook and is suitable for someone pursuing the study of linear algebra as a hobby outside the classroom.