Linear Algebra

Beschreibung

This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations.
The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exercises.
This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations.
The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exercises.
Provides a matrix-oriented approach to the theory of linear algebra including all details and proofs Improves intuition for students in their first contact with abstract concepts Analyzes detailed examples from application, contains ‘MATLAB-Minutes’ and special topics from applied linear algebra Includes supplementary material: sn.pub/extras

Autor*in

Jörg Liesen

Themen in »Linear Algebra«

Linear Algebra Matrices Echelon Form Gaussian Elimination Eigenvalues Linear Maps Vector Spaces Polynomials Fundamental Theorem of Algebra Jordan Canonical Form Matrix Functions Singular Value Decomposition Kronecker Product matrix theory

Stimmen zu »Linear Algebra«

“This book begins with applied problems that are examined as the theory is developed. … Liesen and Mehrmann … present computations with matrix groups and rings, elementary matrices, echelon forms, rank, linear systems, determinants, and eigenvalues and eigenvectors before introducing vectors and vector spaces. … Each chapter ends with a set of exercises addressing both computation and theory. … Summing Up: Recommended. Upper-division undergraduates through professionals/practitioners.” (J. R. Burke, Choice, Vol. 53 (12), September, 2016)

“It provides a good introductory undergraduate course at an intermediate level … . From the beginning, the authors motivate the material with interesting examples … . the text includes short ‘MATLAB-Minutes’ which are exercises providing an informal introduction to the use of MATLAB in linear algebra, including hints about how care may be needed when working in finite precision.” (John D. Dixon, zbMATH 1334.15001, 2016)

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