Advanced Linear Algebra

By: Hugo Woerdeman

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Hardcover | 17 December 2015 | Edition Number 1

At a Glance

Hardcover
352 Pages

Dimensions(cm)
24.3 x 16.3 x 2.7

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Advanced Linear Algebra features a student-friendly approach to the theory of linear algebra. The author's emphasis on vector spaces over general fields, with corresponding current applications, sets the book apart. He focuses on finite fields and complex numbers, and discusses matrix algebra over these fields. The text then proceeds to cover vector spaces in depth. Also discussed are standard topics in linear algebra including linear transformations, Jordan canonical form, inner product spaces, spectral theory, and, as supplementary topics, dual spaces, quotient spaces, and tensor products.

Written in clear and concise language, the text sticks to the development of linear algebra without excessively addressing applications. A unique chapter on "How to Use Linear Algebra" is offered after the theory is presented. In addition, students are given pointers on how to start a research project. The proofs are clear and complete and the exercises are well designed. In addition, full solutions are included for almost all exercises.

Industry Reviews

Woerdeman's work requires background knowledge of linear algebra. Students should be familiar with matrix computations, solving systems, eigenvalues, eigenvectors, finding a basis for the null space, row and column spaces, determinants, and inverses. This text provides a more general approach to vector spaces, developing these over complex numbers and finite fields. Woerdeman (mathematics, Drexel Univ.) provides a review of complex numbers and some basic results for finite fields. This book will help build on previous knowledge obtained from an earlier course and introduce students to numerous advanced topics. A few of these topics are Jordan canonical form, the Cayley-Hamilton Theorem, nilpotent matrices, functions of matrices, Hermitian matrices, the tensor product, quotient space, and dual space. The last chapter, which discusses how to use linear algebra, illustrates some applications, such as finding roots of polynomials, algorithms based on matrix vector products, RSA public key inscription, and theoretical topics, such as the Riemann hypothesis and the "P versus NP problem." Copious exercises are provided, and most give complete solutions. The text will provide a solid foundation for any further work in linear algebra.
--R. L. Pour, Emory and Henry College

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