The book consists of expanded notes of an upper level linear algebra course the author offered. Each section, or lecture, covers about a week’s worth of material and includes a mixture of exercises of interest. So it feels like a series of lectures that is very readable. The notes cover all the basics of linear algebra but from a mature point of view. The author starts by briefly discussing fields and use these axioms to define and explain vector spaces, then carefully explores the relationship between linear transformations and matrices in an easy to understand manner. Determinants are introduced as volume functions and ways 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.Key FeaturesEach section corresponds to about one week or three one-hour lectures, and includes a set of appropriate exercisesAdded a brief final chapter on infinite dimensional vector spaces, including the existence of basis and dimensionMost undergraduate linear algebra courses are not as sophisticated as this one was. Most math graduate students are assumed to have had a good course in linear algebra, but sadly many have not. Reading these notes might be an appropriate way to fill in the gap

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