國立虎尾科技大學 |

Linear Algebra

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Linear Algebra/ by Jörg Liesen, Volker Mehrmann.
Author:	Liesen, Jörg.
other author:	Mehrmann, Volker.
Description:	XI, 324 p. 22 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Matrix theory. -
Online resource:	https://doi.org/10.1007/978-3-319-24346-7
ISBN:	9783319243467

Linear Algebra
Liesen, Jörg.

Linear Algebra[electronic resource] /by Jörg Liesen, Volker Mehrmann. - 1st ed. 2015. - XI, 324 p. 22 illus.online resource. - 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:

1023862
Matrix theory.

LC Class. No.: QA184-205

Dewey Class. No.: 512.5

Linear Algebra
LDR:03092nam a22003975i 4500 001 969454
003 DE-He213
005 20200704001212.0
007 cr nn 008mamaa
008 201211s2015 gw | s |||| 0|eng d
020 $a 9783319243467 $9 978-3-319-24346-7
024 7 $a 10.1007/978-3-319-24346-7 $2 doi
035 $a 978-3-319-24346-7
050 4 $a QA184-205
072 7 $a PBF $2 bicssc
072 7 $a MAT002050 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 512.5 $2 23
100 1 $a Liesen, Jörg. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1261504
245 1 0 $a Linear Algebra $h [electronic resource] / $c by Jörg Liesen, Volker Mehrmann.
250 $a 1st ed. 2015.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a XI, 324 p. 22 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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 Matrix theory. $3 1023862
650 0 $a Algebra. $2 gtt $3 579870
650 1 4 $a Linear and Multilinear Algebras, Matrix Theory. $3 672090
700 1 $a Mehrmann, Volker. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 672515
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319243443
776 0 8 $i Printed edition: $z 9783319243450
830 0 $a Springer Undergraduate Mathematics Series, $x 1615-2085 $3 1255356
856 4 0 $u https://doi.org/10.1007/978-3-319-24346-7
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)