Linear Algebra

Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understanding some of the examples and exercises. This book sets itself apart from other similar textbooks through its dedication to the principle that, whenever possible, definitions and theorems should be stated in a form which is independent of the notion of the dimension of a vector space. A second feature of this book which is worthy of mention is the early introduction of inner product spaces and the associated metric concepts. Students soon feel at ease with this class of spaces because they share so many properties with physical space when equipped with a rectangular coordinate system. Finally, the book includes a chapter concerned with several applications to other fields of the theory that have been developed Content: Front Matter, Page iii Copyright, Page iv Preface, Pages v-vi Symbols, Page x 1 - Vector Spaces, Pages 1-23 2 - Further Properties of Vector Spaces, Pages 24-63 3 - Inner-Product Spaces, Pages 64-92 4 - Linear Transformations, Pages 93-144 5 - Matrices, Pages 145-178 6 - Algebraic Properties of Linear Transformations, Pages 179-230 7 - Bilinear Forms and Quadratic Forms, Pages 231-260 8 - Decomposition Theorems for Normal Transformations, Pages 261-283 9 - Several Applications of Linear Algebra, Pages 284-315 APPENDIX - Notions of Set Theory, Pages 316-321 Index, Pages 322-326