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Advanced Linear Algebra
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Advanced Linear Algebra

Advanced Linear Algebra

Steven Roman - Collection Graduate Texts in Mathematics

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

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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Caractéristiques techniques

  PAPIER
Éditeur(s) Springer
Auteur(s) Steven Roman
Collection Graduate Texts in Mathematics
Parution 02/06/2005
Édition  2eme 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

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