This text begins with an optional chapter on the three main emphases of linear algebra: linear equations, best approximation, and diagonalization. The core of the book presents an axiomatic development of the most important elements of finite-dimensional linear algebra: vector spaces, linear operators, norms and inner products, and determinants and eigenvalues. Case applications show how linear algebra is essential in solving problems involving differentiation equations, optimization, approximation, and combinatorics. Learning features include chapter summaries, basic through advanced exercises, and projects, with answers provided on a web site. Because many of the text's examples involve spaces of functions and elementary calculus, students using the text should have background in linear algebraic equations and calculus. Appendices offer background on the Euclidean algorithm, permutations, polynomials, and analysis in R. Gockenbach teaches at Michigan Technological University. Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)
Linear algebra forms the basis for much of modern mathematics—theoretical, applied, and computational. Finite-Dimensional Linear Algebra provides a solid foundation for the study of advanced mathematics and discusses applications of linear algebra to such diverse areas as combinatorics, differential equations, optimization, and approximation.
The author begins with an overview of the essential themes of the book: linear equations, best approximation, and diagonalization. He then takes students through an axiomatic development of vector spaces, linear operators, eigenvalues, norms, and inner products. In addition to discussing the special properties of symmetric matrices, he covers the Jordan canonical form, an important theoretical tool, and the singular value decomposition, a powerful tool for computation. The final chapters present introductions to numerical linear algebra and analysis in vector spaces, including a brief introduction to functional analysis (infinite-dimensional linear algebra).
Drawing on material from the author’s own course, this textbook gives students a strong theoretical understanding of linear algebra. It offers many illustrations of how linear algebra is used throughout mathematics.
