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Advanced Linear Algebra, 3 Ed.
◆Springer Text Book セール開催中！：2025年8月24日(日)ご注文分まで
※上記表示の販売価格は割引適用後の価格です 出版済み 3週間でお届けいたします。 Series: Graduate Texts in Mathematics, Vol. 135 Author: Steven Roman Publisher: Springer ISBN: 9781441924988 Cover: PAPERBACK Date: 2010年02月 DESCRIPTION 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 TABLE OF CONTENTS 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 最近チェックした商品
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