Advanced linear algebra

Steven Roman

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.

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[目次]

  • 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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この本の情報

書名 Advanced linear algebra
著作者等 Roman, Steven
シリーズ名 Graduate texts in mathematics
出版元 Springer
刊行年月 c2008
版表示 3rd ed
ページ数 xviii, 522 p.
大きさ 25 cm
ISBN 9780387728285
NCID BA84176502
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言語 英語
出版国 アメリカ合衆国
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