Advanced Linear Algebra

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ISBN-13:
9780387728285
Veröffentl:
2007
Erscheinungsdatum:
01.11.2007
Seiten:
525
Autor:
Steven Roman
Gewicht:
972 g
Format:
241x161x38 mm
Serie:
135, Graduate Texts in Mathematics
Sprache:
Englisch
Beschreibung:

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.
This is a graduate level textbook covering an especially broad range of topics. The first part of the book contains a careful but rapid discussion of the basics of linear algebra, including vector spaces, linear transformations, quotient spaces, and isomorphism theorems. The author then proceeds to a discussion of modules, emphasizing a comparison with vector spaces. A thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory follows, 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.
* 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
This graduate level textbook provides encyclopedic treatment of linear algebra theory, both classical and modern. This new edition has been revised and expanded with many new chapters.

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