Advanced Linear Algebra

Steven Roman - Collection Graduate Texts in Mathematics

482 pages, parution le 02/06/2005 (2^eme édition)

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Résumé

This is a graduate 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 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 second part of the book is a collection of topics, including metric vector spaces, metric spaces, Hilbert spaces, tensor products, and affine geometry. The last chapter discusses the umbral calculus, an area of modern algebra with important applications.

The second edition contains two new chapters: a chapter on convexity, separation and positive solutions to linear systems and a chapter on the QR decomposition, singular values and pseudoinverses. The treatments of tensor products and the umbral calculus have been greatly expanded and there is now a discussion of determinants (in the chapter on tensor products), the complexification of a real vector space, Schur's lemma and Gersgorin disks.

L'auteur - Steven Roman

Steven Roman is Professor Emeritus of mathematics at the California State University, Fullerton. Dr. Roman has authored 32 books, including a number of books on mathematics, such as Coding and Information Theory, Advanced Linear Algebra, and Field Theory, published by Springer-Verlag. He has also written a series of 15 small books entitled Modules in Mathematics, designed for thegeneral college-level liberal arts student.

Sommaire

Preface to the Second Edition
Preliminaries
Basic Linear Algebra
- 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
Topics
- 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

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	PAPIER
Éditeur(s)	Springer
Auteur(s)	Steven Roman
Collection	Graduate Texts in Mathematics
Parution	02/06/2005
Édition	2^eme édition
Nb. de pages	482
Format	17 x 24
Couverture	Relié
Poids	817g
Intérieur	Noir et Blanc
EAN13	9780387247663
ISBN13	978-0-387-24766-3