Fundamentals of linear algebra / Katsumi Nomizu

This is a complete treatment of the elements of linear algebra through the Jordan normal form reduction. After an informal heuristic geometric treatment of real 2-dimensional vectors, the author develops the theory of n-dimensional vector spaces over the real or complex field, including treatment of linear mappings and associated matrices, and systems of linear equations. Linear algebra is then temporarily suspended to provide a substantial but condensed chapter on elements of modern algebra—rings, fields (including algebraic extensions), ideals, polynomial algebra, followed by a chapter on determinants treated as alternating linear functions over an arbitrary commutative ring. Chapter 7 then treats eigenvalues, characteristic polynomial and the Jordan normal form. The balance of the book focuses on inner product spaces, affine spaces and Euclidean spaces.
The book is carefully done from a mathematical stand-point. Illustrative examples are frequent and there are reasonably adequate lists of exercises. The latter range from illustrative exercises to more challenging problems, some of which are designed to supplement the textual material. The book contains material adequate for a year-length course, pitched at a fairly abstract level. (MathSciNet)

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