Linear Algebra

By: Kaye, Wilson

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Paperback | 1 January 1998

At a Glance

Paperback
244 Pages

Dimensions(cm)
23.3 x 15.6 x 1.4

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This book covers the basic theory of matrices and vector spaces. The book's three main parts cover (i) matrices, vector spaces, bases and dimension; (ii) inner products bilinear and sesquilinear forms over vector spaces; (iii) linear transformations, eigenvalues and eigenvectors, diagonalization, and Jordan normal form. An introduction to fields and polynomials over fields is also provided, and examples and applications are provided throughout. The approach throughout is rigorous, but without being unnecessarily abstract. In particular, this book would be suitable reading for a student with no prior exposure to abstract algebra. Although intended as a `second course', the book is completely self-contained and all the material usually given in a `first course' is presented fully in Part One, so the book provides a useful guide to the entire theory of vector spaces as usually studied in an undergraduate degree. Abstract methods are illustrated with concrete examples throughout, and more detailed examples highlight applications of linear algebra to analysis, geometry, differential equations, relativity and quantum mechanics. As such, the book provides a valuable introduction to a wide variety of mathematical methods.

Industry Reviews

Kaye offers this work as a second course in linear algebra. As such, it deals with the specific subject matter of linear algebra in a way that could also be viewed as an introduction to abstract algebra or axiomatic mathematics in general. Knowledge of elementary matrix arithmetic and matrix methods--including the general solution to systems of linear equations and computation of inverses and determinants--is assumed, though these topics are briefly reviewed. Some exposure to abstract vector spaces and the notions of basis and dimension would also be helpful to one wishing to peruse this book. For those with a suitable background, this book provides a very rigorous treatment of the fundamentals of linear algebra, including inner product spaces, bilinear and quadratic forms, orthogonal bases, eigenvalues and eigenvectors, and the Jordan canonical form. Certainly appropriate for upper-division undergraduates entertaining thoughts of graduate work in mathematics.--Choice

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