**Translations of Mathematical Monographs**

1998;
303 pp;
Hardcover

MSC: Primary 15; 65;
Secondary 47; 34; 35

Print ISBN: 978-0-8218-0888-7

Product Code: MMONO/175

List Price: $128.00

AMS Member Price: $102.40

MAA Member Price: $115.20

**Electronic ISBN: 978-1-4704-4590-4
Product Code: MMONO/175.E**

List Price: $128.00

AMS Member Price: $102.40

MAA Member Price: $115.20

# Modern Aspects of Linear Algebra

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*S. K. Godunov*

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.

#### Readership

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

#### Table of Contents

# Table of Contents

## Modern Aspects of Linear Algebra

- Cover Cover11
- Title page v6
- Contents vii8
- Preface xi12
- Introduction 118
- Euclidean linear spaces 320
- Orthogonal and unitary linear transformations 1532
- Orthogonal and unitary transformations. Singular values 2542
- Matrices of operators in the Euclidean space 4562
- Unitary similar transformations. The Schur theorem 4764
- Alternation theorems 5976
- The Weyl inequalities 87104
- Variational principles 101118
- Resolvent and dichotomy of spectrum 123140
- Quadratic forms in the spectrum dichotomy problem 139156
- Matrix equations and projections 151168
- The Hausdorff set of a matrix 183200
- Application of spectral analysis. The most important algorithms 213230
- Matrix operators as models of differential operators 215232
- Application of the theory of functions of complex variables 235252
- Computational algorithms of spectral analysis 257274
- Bibliography 301318
- Index 303320
- Back Cover Back Cover1321