Linear Algebra

This popular and successful text was originally written for a one-semester course in linearalgebra at the sophomore undergraduate level. Consequently, the book deals almostexclusively with real finite dimensional vector spaces, but in a setting and formulationthat permits easy generalization to abstract vector spaces. A wide selection of examplesof vector spaces and linear transformation is presented to serve as a testing groundfor the theory. In the second edition, a new chapter on Jordan normal form was added which reappears here in expanded form as the second goal of this new edition, after theprincipal axis theorem. To achieve these goals in one semester it is necessary to followa straight path, but this is compensated by a wide selection of examples and exercises.In addition, the author includes an introduction to invariant theory to show that linearalgebra alone is incapable of solving these canonical forms problems. This bookis a compact butmathematically clean introduction to linear algebra with particular emphasis on topics inabstract algebra, the theory of differential equations, and group representation theory.