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Linear algebra

Liesen, Jorg.

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Linear algebra

Record Type:	Electronic resources : Monograph/item
Title/Author:	Linear algebra/ by Jorg Liesen, Volker Mehrmann.
Author:	Liesen, Jorg.
other author:	Mehrmann, Volker.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	xi, 324 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Algebras, Linear. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-24346-7
ISBN:	9783319243467

Linear algebra
Liesen, Jorg.

Linear algebra[electronic resource] /by Jorg Liesen, Volker Mehrmann. - Cham :Springer International Publishing :2015. - xi, 324 p. :ill., digital ;24 cm. - Springer undergraduate mathematics series,1615-2085. - Springer undergraduate mathematics series..

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.

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.

ISBN: 9783319243467

Standard No.: 10.1007/978-3-319-24346-7doiSubjects--Topical Terms:

521915
Algebras, Linear.

LC Class. No.: QA184.2

Dewey Class. No.: 512.5

Linear algebra
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100 1 $a Liesen, Jorg. $3 2163026
245 1 0 $a Linear algebra $h [electronic resource] / $c by Jorg Liesen, Volker Mehrmann.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xi, 324 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer undergraduate mathematics series, $x 1615-2085
505 0 $a 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.
520 $a 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.
650 0 $a Algebras, Linear. $3 521915
650 0 $a Mathematics. $3 515831
650 0 $a Matrix theory. $3 2058364
650 0 $a Algebra. $3 516203
650 2 4 $a Linear and Multilinear Algebras, Matrix Theory. $3 891082
700 1 $a Mehrmann, Volker. $3 897536
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Springer undergraduate mathematics series. $3 1567980
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-24346-7
950 $a Mathematics and Statistics (Springer-11649)