Advanced linear algebra
Author(s)
Bibliographic Information
Advanced linear algebra
（Graduate texts in mathematics, 135）
Springer, c2008
3rd ed
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Note
Includes bibliographical references (p. [507]-511) and index
Description and Table of Contents
Description
This graduate level textbook covers an especially broad range of topics. The book first offers a careful discussion of the basics of linear algebra. It then proceeds to a discussion of modules, emphasizing a comparison with vector spaces, and presents a thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory, culminating in the finite dimensional spectral theorem for normal operators. The new edition has been revised and contains a chapter on the QR decomposition, singular values and pseudoinverses, and a chapter on convexity, separation and positive solutions to linear systems.
Table of Contents
* Vector Spaces * Linear Transformations * The Isomorphism Theorems * Modules I: Basic Properties * Modules II: Free and Noetherian Modules * Modules over a Principal Ideal Domain * The Structure of a Linear Operator * Eigenvalues and Eigenvectors * Real and Complex Inner Product Spaces * Structure Theory for Normal Operators * Metric Vector Spaces: The Theory of Bilinear Forms * Metric Spaces * Hilbert Spaces * Tensor Products * Positive Solutions to Linear Systems: Convexity and Separation * Affine Geometry * Operator Factorizations: QR and Singular Value * The Umbral Calculus * References * Index
by "Nielsen BookData"
