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Modern Aspects of Linear Algebra

About this Title

S. K. Godunov, Russian Academy of Sciences, Novosibirsk, Russia. Translated by Tamara Rozhkovskaya

Publication: Translations of Mathematical Monographs
Publication Year: 1998; Volume 175
ISBNs: 978-0-8218-0888-7 (print); 978-1-4704-4590-4 (online)
DOI: https://doi.org/10.1090/mmono/175
MathSciNet review: MR1620203
MSC: Primary 15-02; Secondary 47Axx, 65Fxx

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Table of Contents

Front/Back Matter

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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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