## Linear Algebra

**Author(s):**

Jörg Liesen, Volker Mehrmann

**Publisher:**

Springer

**Pages:**324

**Further Actions:**

**Categories:**

### AVAILABLE FORMATS

Paperback - 9783319243443

28 November 2015

* $44.99*

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**In stock**

Ebook - 9783319243467

20 November 2015

* $34.99*

**In stock**

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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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.

“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)