Advanced Linear Algebra - Roman Steven | Libro Springer 10/2007 - HOEPLI.it


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roman steven - advanced linear algebra

Advanced Linear Algebra




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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Springer

Pubblicazione: 10/2007
Edizione: 3rd ed. 2008





Trama

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.

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 and a theorem to the effect that , dim(V)<=dim(V*) with equality if and only if V is finite-dimensional;

* 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





Sommario

* 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




Autore

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.








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Altre Informazioni

ISBN:

9780387728285

Condizione: Nuovo
Collana: Graduate Texts in Mathematics
Dimensioni: 235 x 155 mm Ø 2070 gr
Formato: Copertina rigida
Illustration Notes:23 schw.-w. Abb., 23 schw.-w. Zeichn.
Pagine Arabe: 525
Pagine Romane: xviii






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