Hardcover ISBN:  9780821808887 
Product Code:  MMONO/175 
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eBook ISBN:  9781470445904 
Product Code:  MMONO/175.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821808887 
eBook: ISBN:  9781470445904 
Product Code:  MMONO/175.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 
Hardcover ISBN:  9780821808887 
Product Code:  MMONO/175 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445904 
Product Code:  MMONO/175.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821808887 
eBook ISBN:  9781470445904 
Product Code:  MMONO/175.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 175; 1998; 303 ppMSC: Primary 15; 65; Secondary 47; 34; 35
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.
ReadershipGraduate students and research mathematicians working in linear algebra, differential equations, applied mathematics, and computational physics.

Table of Contents

Introduction

Euclidean linear spaces

Orthogonal and unitary linear transformations

Orthogonal and unitary transformations. Singular values

Matrices of operators in the Euclidean space

Unitary similar transformations. The Schur theorem

Alternation theorems

The Weyl inequalities

Variational principles

Resolvent and dichotomy of spectrum

Quadratic forms in the spectrum dichotomy problem

Matrix equations and projections

The Hausdorff set of a matrix

Application of spectral analysis. The most important algorithms

Matrix operators as models of differential operators

Application of the theory of functions of complex variables

Computational algorithms of spectral analysis


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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.
Graduate students and research mathematicians working in linear algebra, differential equations, applied mathematics, and computational physics.

Introduction

Euclidean linear spaces

Orthogonal and unitary linear transformations

Orthogonal and unitary transformations. Singular values

Matrices of operators in the Euclidean space

Unitary similar transformations. The Schur theorem

Alternation theorems

The Weyl inequalities

Variational principles

Resolvent and dichotomy of spectrum

Quadratic forms in the spectrum dichotomy problem

Matrix equations and projections

The Hausdorff set of a matrix

Application of spectral analysis. The most important algorithms

Matrix operators as models of differential operators

Application of the theory of functions of complex variables

Computational algorithms of spectral analysis