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Modern Aspects of Linear Algebra
S. K. Godunov, Russian Academy of Sciences, Novosibirsk, Russia
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Translations of Mathematical Monographs
1998; 303 pp; hardcover
Volume: 175
ISBN-10: 0-8218-0888-5
ISBN-13: 978-0-8218-0888-7
List Price: US$128
Member Price: US$102.40
Order Code: MMONO/175
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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.

Readership

Graduate 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 variable
  • Computational algorithms of spectral analysis
  • Bibliography
  • Index
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