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Linear algebra

Author: Jörg Liesen; V L Mehrmann
Publisher: Cham : Springer, 2015.
Series: Springer undergraduate mathematics series
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jörg Liesen; V L Mehrmann
ISBN: 9783319243467 3319243462
OCLC Number: 932169329
Description: 1 online resource (xi, 324 pages) : color illustrations.
Contents: Linear Algebra in every day life --
Basic mathematical concepts --
Algebraic structures --
Matrices --
The echelon form and the rank of matrices --
Linear systems of equations --
Determinants of matrices --
The characteristic polynomial and eigenvalues of matrices --
Vector spaces --
Linear maps --
Linear forms and bilinear forms --
Euclidean and unitary vector spaces --
Adjoints of linear maps --
Eigenvalues of endomorphisms --
Polynomials and the Fundamental Theorem of Algebra --
Cyclic subspaces, duality and the Jordan canonical form --
Matrix functions and systems of differential equations --
Special classes of endomorphisms --
The singular value decomposition --
The Kronecker product and linear matrix equations.
Series Title: Springer undergraduate mathematics series
Responsibility: by Jörg Liesen, Volker Mehrmann.

Abstract:

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.

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"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 Read more...

 
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