This textbook is directed towards students who are familiar with
matrices and their use in solving systems of linear equations. The
emphasis is on the algebra supporting the ideas that make linear
algebra so important, both in theoretical and practical
applications. The narrative is written to bring along students who
may be new to the level of abstraction essential to a working
understanding of linear algebra. The determinant is used
throughout, placed in some historical perspective, and defined
several different ways, including in the context of exterior
algebras. The text details proof of the existence of a basis for an
arbitrary vector space and addresses vector spaces over arbitrary
fields. It develops LU-factorization, Jordan canonical form, and
real and complex inner product spaces. It includes examples of
inner product spaces of continuous complex functions on a real
interval, as well as the background material that students may need
in order to follow those discussions. Special classes of matrices
make an entrance early in the text and subsequently appear
throughout. The last chapter of the book introduces the classical
groups.
General
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