This book consists of the expanded notes from an upper level linear
algebra course given some years ago by the author. Each section, or
lecture, covers about a week's worth of material and includes a
full set of exercises of interest. It should feel like a very
readable series of lectures. The notes cover all the basics of
linear algebra but from a mature point of view. The author starts
by briefly discussing fields and uses those axioms to define and
explain vector spaces. Then he carefully explores the relationship
between linear transformations and matrices. Determinants are
introduced as volume functions and as a way to determine whether
vectors are linearly independent. Also included is a full chapter
on bilinear forms and a brief chapter on infinite dimensional
spaces.The book is very well written, with numerous examples and
exercises. It includes proofs and techniques that the author has
developed over the years to make the material easier to understand
and to compute.
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