Linear Algebra

This popular and successful text was originally written for a one semestercourse in linear algebra at the sophomore undergraduate level. Students at thislevel g... » 

This popular and successful text was originally written for a one semestercourse in linear algebra at the sophomore undergraduate level. Students at thislevel generally have had little contact with complex numbers or abstractmathematics so the book deals almost exclusively with real finite dimensionalvector spaces but in a setting and formulation that permits easygeneralization to abstract vector spaces. The goal of the first two editionswas the principal axis theorem for real symmetric linear transformation. Theprincipal axis theorem becomes the first of two goals for this new editionwhich follows a straight path to its solution. A wide selection of examples ofvector spaces and linear transformation is presented to serve as a testingground for the theory. In the second edition a new chapter on Jordan normalform was added which reappears here in expanded form as the second goal of thisnew edition along with applications to differential systems. To achieve theprincipal axis theorem in one semester a straight path to these two goals isfollowed. As compensation there is a wide selection of examples and exercises.In addition the author includes an introduction to invariant theory to showstudents that linear algebra alone is not capable of solving these canonicalforms problems. The book continues to offer a compact but mathematically cleanintroduction to linear algebra with particular emphasis on topics that are usedin abstract algebra the theory of differential equations and grouprepresentation theory. «