Advanced Linear Algebra, Second Edition (Graduate Texts in Mathematics, 135)

Roman, Steven

ISBN 10: 0387247661 / ISBN 13: 9780387247663

Published by Springer, Irvine, California, U.S.A., 2005

About this Item

Graduate Texts in Mathematics, 135. Hardcover in very good condition. A couple of minor markings to page block face, no other notable flaws. Pages are clean, and text and illustrations are clear. TH.

Seller Inventory # 531464

Bibliographic Details

• Title: Advanced Linear Algebra, Second Edition (Graduate Texts in Mathematics, 135)
• Publisher: Springer, Irvine, California, U.S.A.
• Publication Date: 2005
• Language: English
• ISBN 10: 0387247661
• ISBN 13: 9780387247663
• Binding: Hardcover
• Edition: Second Edition.
• Condition: Very Good
• Dust Jacket Condition: No Dust Jacket
• Book Type: Used
• Seller catalogs:
  • Mathematics/Accounting

About this title

Synopsis

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.

About the Author

Dr. Roman has authored 32 books, including a number of books on mathematics, such as Introduction to the Finance of Mathematics, Coding and Information Theory, and Field Theory, published by Springer-Verlag. He has also written Modules in Mathematics, a series of 15 small books designed for the general college-level liberal arts student. Besides his books for O'Reilly, Dr. Roman has written two other computer books, both published by Springer-Verlag.