Translations of Mathematical Monographs 1998; 303 pp; hardcover Volume: 175 ISBN10: 0821808885 ISBN13: 9780821808887 List Price: US$128 Member Price: US$102.40 Order Code: MMONO/175
 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
