Titlebook: Numerical Linear Algebra: Theory and Applications; Larisa Beilina,Evgenii Karchevskii,Mikhail Karchev Textbook 2017 Springer International

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认识

Textbook 2017oped from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigenproblems. Numer

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责难

Canonical Forms and Factorizations,ed. A special section is devoted to studying matrix pencils. We obtain their canonical forms and describe applications to investigate the structure of solutions of systems of ordinary linear differential equations.

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Preliminaries, roots. We introduce the concept of determinants, establish their properties, and present the basic theory of systems of linear algebraic equations with nonsingular matrices. The main types of rectangular matrices are described.

Expiration

Vector Spaces,then a one-to-one correspondence between geometric vectors and ordered triples of real numbers (the coordinates of vectors in the basis) is determined, and algebraic operations with vector coordinates can be substituted for geometric operations with the vectors themselves.

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Linear Operators,e-dimensional linear spaces. We give a detailed investigation of their spectral properties. Special attention is paid to the study of the structure of the main classes of linear operators in finite-dimensional Euclidean and unitary spaces.

善于

Algorithms for the Nonsymmetric Eigenvalue Problem,applied to dense matrices, and iterative methods such as the Rayleigh–Ritz method and Lanczos’s algorithm are applied to sparse matrices. Iterative methods usually can compute not all of the eigenvalues and eigenvectors, but only some subset, and their convergence depends on the structure of the matrix.

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