Advanced linear algebra / Steven Roman.

AUTOR: Steven Roman
ISBN: 9780387728285
EDITOR: Springer
IDIOMA: eng
PÁGINAS: XVIII, 522
AÑO: 2008

 
   
RECOMENDADO EN LAS SIGUIENTES ASIGNATURAS
Álgebra lineal

 
RESUMEN

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 Contains topics that are not generally found in linear algebra books Coverage is especially broad An extensive bibliography has been added Encyclopedic treatment of linear algebra theory, both classical and modern
 
INDICE

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.