Linear Algebra / by Jörg Liesen, Volker Mehrmann.

Format:

Book

Author/Creator:

Liesen, Jörg, Author.

Mehrmann, Volker., Author.

Series:

Springer Undergraduate Mathematics Series, 2197-4144

Language:

English

Subjects (All):

Algebras, Linear.

Linear Algebra.

Local Subjects:

Linear Algebra.

Physical Description:

1 online resource (XI, 324 p. 22 illus.)

Edition:

1st ed. 2015.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2015.

Language Note:

English

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 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.

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

ISBN:

9783319243467

3319243462

OCLC:

932169329