Modern Aspects of Linear Algebra: Translations of Mathematical Monographs / Edition 1

Modern Aspects of Linear Algebra: Translations of Mathematical Monographs / Edition 1

by S. K. Godunov
     
 

ISBN-10: 0821808885

ISBN-13: 9780821808887

Pub. Date: 05/05/1998

Publisher: American Mathematical Society

This book discusses fundamental ideas of linear algebra. The author presents the spectral theory of nonselfadjoint matrix operators and matrix pencils in a finite dimensional Euclidean space. Statements of computational problems and brief descriptions of numerical algorithms, some of them nontraditional, are given. Proved in detail are classical problems that are

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Overview

This book discusses fundamental ideas of linear algebra. The author presents the spectral theory of nonselfadjoint matrix operators and matrix pencils in a finite dimensional Euclidean space. Statements of computational problems and brief descriptions of numerical algorithms, some of them nontraditional, are given. Proved in detail are classical problems that are not usually found in standard university courses. In particular, the material shows the role of delicate estimates for the resolvent of an operator and underscores the need for the study and use of such estimates in numerical analysis.

Product Details

ISBN-13:
9780821808887
Publisher:
American Mathematical Society
Publication date:
05/05/1998
Series:
Translations of Mathematical Monographs Series, #175
Pages:
303
Product dimensions:
7.48(w) x 10.63(h) x (d)

Table of Contents

Preface
Pt. 1Introduction1
Ch. 1Euclidean Linear Spaces3
Ch. 2Orthogonal and Unitary Linear Transformations15
Ch. 3Orthogonal and Unitary Transformations. Singular Values25
Pt. 2Matrices of Operators in the Euclidean Space45
Ch. 4Unitary Similar Transformations. The Schur Theorem47
Ch. 5Alternation Theorems59
Ch. 6The Weyl Inequalities87
Ch. 7Variational Principles101
Ch. 8Resolvent and Dichotomy of Spectrum123
Ch. 9Quadratic Forms in the Spectrum Dichotomy Problem139
Ch. 10Matrix Equations and Projections151
Ch. 11The Hausdorff Set of a Matrix183
Pt. 3Application of Spectral Analysis. Most Important Algorithms213
Ch. 12Matrix Operators as Models of Differential Operators215
Ch. 13Application of the Theory of Functions of Complex Variables235
Ch. 14Computational Algorithms of Spectral Analysis257
Bibliography301
Index303

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