This book presents a substantial part of matrix analysis that is functional analytic in spirit. Topics covered include the theory of majorization, variational principles for eigenvalues, operator monotone and convex functions, and perturbation of matrix functions and matrix inequalities. The book offers several powerful methods and techniques of wide applicability, and it discusses connections with other areas of mathematics.
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"A highly readable and attractive account of the subject. The book is a must for anyone working in matrix analysis; it can be recommended to graduate students as well as to specialists."—ZENTRALBLATT MATH
"There is an ample selection of exercises carefully positioned throughout the text. In addition each chapter includes problems of varying difficulty in which themes from the main text are extended."—MATHEMATICAL REVIEWSContenuti:
I A Review of Linear Algebra.- I.1 Vector Spaces and Inner Product Spaces.- I.2 Linear Operators and Matrices.- I.3 Direct Sums.- I.4 Tensor Products.- I.5 Symmetry Classes.- I.6 Problems.- I.7 Notes and References.- II Majorisation and Doubly Stochastic Matrices.- II.1 Basic Notions.- II. 2 Birkhoff’s Theorem.- II.3 Convex and Monotone Functions.- II.4 Binary Algebraic Operations and Majorisation.- II.5 Problems.- II.6 Notes and References.- III Variational Principles for Eigenvalues.- III.1 The Minimax Principle for Eigenvalues.- III.2 Weyl’s Inequalities.- III.3 Wielandt’s Minimax Principle.- III.4 Lidskii’s Theorems.- III. 5 Eigenvalues of Real Parts and Singular Values.- III.6 Problems.- III.7 Notes and References.- IV Symmetric Norms.- IV.l Norms on ?n.- IV.2 Unitarily Invariant Norms on Operators on ?n.- IV.3 Lidskii’s Theorem (Third Proof).- IV.4 Weakly Unitarily Invariant Norms.- IV.5 Problems.- IV.6 Notes and References.- V Operator Monotone and Operator Convex Functions.- V.1 Definitions and Simple Examples.- V.2 Some Characterisations.- V.3 Smoothness Properties.- V.4 Loewner’s Theorems.- V.5 Problems.- V.6 Notes and References.- VI Spectral Variation of Normal Matrices.- VI. 1 Continuity of Roots of Polynomials.- VI. 2 Hermitian and Skew-Hermitian Matrices.- VI. 3 Estimates in the Operator Norm.- VI. 4 Estimates in the Frobenius Norm.- VI. 5 Geometry and Spectral Variation: the Operator Norm.- VI. 6 Geometry and Spectral Variation: wui Norms.- VI. 7 Some Inequalities for the Determinant.- VI. 8 Problems.- VI. 9 Notes and References.- VII Perturbation of Spectral Subspaces of Normal Matrices.- VII. 1 Pairs of Subspaces.- VII. 2 The Equation AX — XB = Y.- VII. 3 Perturbation of Eigenspaces.- VII. 4 A Perturbation Bound for Eigenvalues.- VII. 5 Perturbation of the Polar Factors.- VII. 6 Appendix: Evaluating the (Fourier) constants.- VII. 7 Problems.- VII. 8 Notes and References.- VIII Spectral Variation of Nonnormal Matrices.- VIII. 1 General Spectral Variation Bounds.- VIII. 4 Matrices with Real Eigenvalues.- VIII. 5 Eigenvalues with Symmetries.- VIII. 6 Problems.- VIII. 7 Notes and References.- IX A Selection of Matrix Inequalities.- IX. 1 Some Basic Lemmas.- IX. 2 Products of Positive Matrices.- IX. 3 Inequalities for the Exponential Function.- IX. 4 Arithmetic-Geometric Mean Inequalities.- IX. 5 Schwarz Inequalities.- IX. 6 The Lieb Concavity Theorem.- IX. 7 Operator Approximation.- IX. 8 Problems.- IX. 9 Notes and References.- X Perturbation of Matrix Functions.- X. 1 Operator Monotone Functions.- X. 2 The Absolute Value.- X. 3 Local Perturbation Bounds.- X. 4 Appendix: Differential Calculus.- X. 5 Problems.- X. 6 Notes and References.- References.
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Descrizione libro Condizione libro: New. This is an International Edition Brand New Paperback Same Title Author and Edition as listed. ISBN and Cover design differs. Similar Contents as U.S Edition. Standard Delivery within 6-14 business days ACROSS THE GLOBE. We can ship to PO Box address in US. International Edition Textbooks may bear a label "Not for sale in the U.S. or Canada" or "For sale in Asia only" or similar restrictions- printed only to discourage students from obtaining an affordable copy. US Court has asserted your right to buy and use International edition. Access code/CD may not provided with these editions. We may ship the books from multiple warehouses across the globe including Asia depending upon the availability of inventory. Printed in English. Customer satisfaction guaranteed. Codice libro della libreria NU3_9788181282293
Descrizione libro Springer. Condizione libro: New. 0387948465 This is an International Edition. Brand New, Paperback, Delivery within 6-14 business days, Similar Contents as U.S Edition, ISBN and Cover design may differ, printed in Black & White. Choose Expedited shipping for delivery within 3-8 business days. We do not ship to PO Box, APO , FPO Address. In some instances, subjects such as Management, Accounting, Finance may have different end chapter case studies and exercises. International Edition Textbooks may bear a label "Not for sale in the U.S. or Canada" and "Content may different from U.S. Edition" - printed only to discourage U.S. students from obtaining an affordable copy. The U.S. Supreme Court has asserted your right to purchase international editions, and ruled on this issue. Access code/CD is not provided with these editions , unless specified. We may ship the books from multiple warehouses across the globe, including India depending upon the availability of inventory storage. Customer satisfaction guaranteed. Codice libro della libreria UM9780387948461
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Descrizione libro Springer, 1996. Hardback. Condizione libro: NEW. 9780387948461 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0275601