Advanced Linear Algebra (Graduate Texts in Mathematics v. 135 3rd ed. 2008)
By: Steven Roman (author)Hardback
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This graduate level textbook covers an especially broad range of topics. The book first offers a careful discussion of the basics of linear algebra. It then proceeds to a discussion of modules, emphasizing a comparison with vector spaces, and presents a thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory, 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.
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.
Preface to the third edition.- Preface to the second edition.- Preface to the first edition.- Preliminaries.- 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.- Singular values and the moore-penrose inverse.- An introduction to algebras.- The umbral calculus.- References.- Index of symbols.- Index
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- ID: 9780387728285
3rd ed. 2008
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