Linear Algebra

This text is written for a course in linear algebra at the (U.S.) sophomore undergraduate level, preferably directly following a one-variable calculus course, so that linear algebra can be used in a course on multidimensional calculus.

Realizing that students at this level have had little contact with complex numbers or abstract mathematics the book deals almost exclusively with real finite-dimensional vector spaces in a setting and formulation that permits easy generalization to abstract vector spaces.

The parallel complex theory is developed in the exercises.

The book has as a goal the principal axis theorem for real symmetric transformations, and a more or less direct path is followed.

As a consequence there are many subjects that are not developed, and this is intentional.

However a wide selection of examples of vector spaces and linear trans- formations is developed, in the hope that they will serve as a testing ground for the theory.

The book is meant as an introduction to linear algebra and the theory developed contains the essentials for this goal.

Students with a need to learn more linear algebra can do so in a course in abstract algebra, which is the appropriate setting.

Through this book they will be taken on an excursion to the algebraic/analytic zoo, and introduced to some of the animals for the first time.

Further excursions can teach them more about the curious habits of some of these remarkable creatures.