Detailsuche

Advanced Linear Algebra

Advanced Linear Algebra
-0 %
Steven Roman
Springer-Verlag GmbH
Sofort lieferbar | Lieferzeit: Sofort lieferbar I

Unser bisheriger Preis:ORGPRICE: 59,87 €

Jetzt 59,86 €*

Alle Preise inkl. MwSt. | Versandkostenfrei
Artikel-Nr:
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:

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.

For the third edition, the author has added a new chapter on associative algebras that includes the well known characterizations of the finite-dimensional division algebras over the real field (a theorem of Frobenius) and over a finite field (Wedderburn's theorem); polished and refined some arguments (such as the discussion of reflexivity, the rational canonical form, best approximations and the definitions of tensor products); upgraded some proofs that were originally done only for finite-dimensional/rank cases; added new theorems, including the spectral mapping theorem; corrected all known errors; the reference section has been enlarged considerably, with over a hundred references to books on linear algebra.

From the reviews of the second edition:

"In this 2nd edition, the author has rewritten the entire book and has added more than 100 pages of new materials. ... As in the previous edition, the text is well written and gives a thorough discussion of many topics of linear algebra and related fields. ... the exercises are rewritten and expanded. ... Overall, I found the book a very useful one. ... It is a suitable choice as a graduate text or as a reference book."

Ali-Akbar Jafarian, ZentralblattMATH

"This is a formidable volume, a compendium of linear algebra theory, classical and modern ... . The development of the subject is elegant ... . The proofs are neat ... . The exercise sets are good, with occasional hints given for the solution of trickier problems. ... It represents linear algebra and does so comprehensively."

Henry Ricardo, MathDL

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.
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.
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.- Singular Values and the Moore-Penrose Inverse.- An Introduction to Algebras.- The Umbral Calculus.

Kunden Rezensionen

Zu diesem Artikel ist noch keine Rezension vorhanden.
Helfen sie anderen Besuchern und verfassen Sie selbst eine Rezension.
> neue Rezension schreiben