Linear Algebra II

Foundations and Applications: Eigenvalues and Geometry
Artikelnummer: 978-3-032-41476-2
Einband: Fester Einband
Verfügbarkeit: Noch nicht erschienen, Februar 2027
CHF 96.00
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These volumes introduce and develop the theory of linear structures for students of mathematics and its applications. Today, linear algebra serves as an essential tool and unifying language across nearly all areas of mathematics. Given its importance in the natural sciences, engineering, and economics, linear algebra is presented as a valuable and widely applicable subject in its own right.

In addition to the standard core material, the volume includes topics of interest to students from a variety of disciplines. Students of mathematics education will find an introduction to several aspects of analytic geometry. In this second volume, the study of analytic geometry is extended through a treatment of quadrics and, in particular, the theory of polyhedra, culminating in linear optimization and the simplex algorithm. Readers with an interest in algebra are introduced to bi- and multilinear forms and multilinear algebra, while those interested in analysis or physics will find a thorough treatment of spectral theory and linear ordinary differential equations. The Schur and Jordan normal forms, including their real counterparts, are fundamental to the development of the theory.

Throughout, structural insights are combined with practical algorithmic methods. The treatment of tensor calculus helps bridge the gap between the mathematical and engineering perspectives, while convex geometry facilitates the transition to functional analysis and its applications. Students pursuing numerical mathematics, optimization, or data-oriented applications will encounter topics such as singular value decomposition, principal component analysis, and linear and quadratic optimization. Numerical methods are further developed through the study of least-squares problems and QR decomposition, providing a foundation for the modern eigenvalue algorithms described in Volume 3. Many of these topics are also of special relevance to students of economics and related disciplines.

Particular emphasis is placed on connecting theory and algorithms and on relating both to applications in the sciences. To support this goal, mathematical modelling plays a central role. Ongoing examples drawn from mechanics, electrical networks, and economics are developed progressively alongside the theory.


EUDR exemption - product or manufacturing materials placed on the market prior to 31.12.2025.

These volumes introduce and develop the theory of linear structures for students of mathematics and its applications. Today, linear algebra serves as an essential tool and unifying language across nearly all areas of mathematics. Given its importance in the natural sciences, engineering, and economics, linear algebra is presented as a valuable and widely applicable subject in its own right.

In addition to the standard core material, the volume includes topics of interest to students from a variety of disciplines. Students of mathematics education will find an introduction to several aspects of analytic geometry. In this second volume, the study of analytic geometry is extended through a treatment of quadrics and, in particular, the theory of polyhedra, culminating in linear optimization and the simplex algorithm. Readers with an interest in algebra are introduced to bi- and multilinear forms and multilinear algebra, while those interested in analysis or physics will find a thorough treatment of spectral theory and linear ordinary differential equations. The Schur and Jordan normal forms, including their real counterparts, are fundamental to the development of the theory.

Throughout, structural insights are combined with practical algorithmic methods. The treatment of tensor calculus helps bridge the gap between the mathematical and engineering perspectives, while convex geometry facilitates the transition to functional analysis and its applications. Students pursuing numerical mathematics, optimization, or data-oriented applications will encounter topics such as singular value decomposition, principal component analysis, and linear and quadratic optimization. Numerical methods are further developed through the study of least-squares problems and QR decomposition, providing a foundation for the modern eigenvalue algorithms described in Volume 3. Many of these topics are also of special relevance to students of economics and related disciplines.

Particular emphasis is placed on connecting theory and algorithms and on relating both to applications in the sciences. To support this goal, mathematical modelling plays a central role. Ongoing examples drawn from mechanics, electrical networks, and economics are developed progressively alongside the theory.


EUDR exemption - product or manufacturing materials placed on the market prior to 31.12.2025.
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VerlagSpringer International Publishing
EinbandFester Einband
Erscheinungsjahr2027
Seitenangabe304 S.
AusgabekennzeichenEnglisch
AbbildungenApprox. 405 p. 25 illus., schwarz-weiss Illustrationen
MasseH23.5 cm x B15.5 cm
CoverlagSpringer (Imprint/Brand)
AutorKnabner, Peter / Barth, Wolf

Über den Autor Peter Knabner

Peter Knabner is Professor emeritus at the University of Erlangen-Nürnberg, where he has led the chair Applied Mathematics I from 1994 to 2020, and also guest professor at the cluster of excellence SimTech of the University of Stuttgart. Knabner'research is focussed on the derivation, analysis and numerical approximation of mathematical models for flow and transport in porous media. with applications in science and technology, in particular in hydrogeology. After the study of Mathematics and Computer Science at the Freie Universität Berlin (diploma in 1972) he earned a PhD from the University of Augsburg in 1983, where he also received a higher doctoral degree (habilitation) in 1988. Peter Knabner is author of more than 180 peer-reviewed publications in applied analysis, numerical mathematics and geohydrology. He is author and co-author of 13 research monographs and textbooks in German and English. Lutz Angermann is Professor of Numerical Mathematics at the Department of Mathematics of the Clausthal University of Technology since 2001. His research is concerned with the development and mathematical analysis of numerical methods for solving partial differential equations with special interests in finite volume and finite element methods and their application to problems in Physics and Engineering. After the study of Mathematics at the State University of Kharkov (now V.N. Karazin Kharkiv National University, Ukraine) he earned a PhD from the University of Technology at Dresden in 1987. The University of Erlangen-Nürnberg awarded him a higher doctoral degree (habilitation) in 1995. From 1998 to 2001, he held the post of an Associate Professor of Numerical Mathematics at the University of Magdeburg. He has authored or co-authored about 100 scientific papers, among them four books as co-author, and he edited two books.

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