Indefinite Linear Algebra And Applications

Author : Israel Gohberg,Peter Lancaster,Leiba Rodman
Publisher : Springer Science & Business Media
Page : 357 pages
File Size : 46,8 Mb
Release : 2006-02-08
Category : Mathematics
ISBN : 9783764373504

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Indefinite Linear Algebra and Applications by Israel Gohberg,Peter Lancaster,Leiba Rodman Pdf

This book covers recent results in linear algebra with indefinite inner product. It includes applications to differential and difference equations with symmetries, matrix polynomials and Riccati equations. These applications are based on linear algebra in spaces with indefinite inner product. The latter forms an independent branch of linear algebra called indefinite linear algebra. This new subject is presented following the principles of a standard linear algebra course.

Author : Leiba Rodman
Publisher : Princeton University Press
Page : 384 pages
File Size : 43,6 Mb
Release : 2014-08-24
Category : Mathematics
ISBN : 9781400852741

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Topics in Quaternion Linear Algebra by Leiba Rodman Pdf

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

Author : John T. Scheick
Publisher : McGraw-Hill Science, Engineering & Mathematics
Page : 464 pages
File Size : 40,9 Mb
Release : 1997
Category : Algebras, Linear
ISBN : UOM:49015002972272

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Linear Algebra with Applications by John T. Scheick Pdf

Designed for the second level course in linear algebra taken by your junior- or senior-level mathematics, engineering, or science majors, this text focuses on the fundamentals of linear algebra in a thematic framework which emphasizes concepts most important to applied mathematics, engineering, and science.

Author : Israel Gohberg,M. G. Krein
Publisher : American Mathematical Soc.
Page : 444 pages
File Size : 54,7 Mb
Release : 2024-05-23
Category : Mathematics
ISBN : 0821886541

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Theory and Applications of Volterra Operators in Hilbert Space by Israel Gohberg,M. G. Krein Pdf

An abstract Volterra operator is, roughly speaking, a compact operator in a Hilbert space whose spectrum consists of a single point $\lambda=0$. The theory of abstract Volterra operators, significantly developed by the authors of the book and their collaborators, represents an important part of the general theory of non-self-adjoint operators in Hilbert spaces. The book, intended for all mathematicians interested in functional analysis and its applications, discusses the main ideas and results of the theory of abstract Volterra operators. Of particular interest to analysts and specialists in differential equations are the results about analytic models of abstract Volterra operators and applications to boundary value problems for ordinary differential equations.

Author : Aldo G. S. Ventre
Publisher : Springer Nature
Page : 530 pages
File Size : 54,8 Mb
Release : 2023-02-11
Category : Technology & Engineering
ISBN : 9783031205491

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Calculus and Linear Algebra by Aldo G. S. Ventre Pdf

This textbook offers a comprehensive coverage of the fundamentals of calculus, linear algebra and analytic geometry. Intended for bachelor’s students in science, engineering, architecture, economics, the presentation is self-contained, and supported by numerous graphs, to facilitate visualization and also to stimulate readers’ intuition. The proofs of the theorems are rigorous, yet presented in straightforward and comprehensive way. With a good balance between algebra, geometry and analysis, this book guides readers to apply the theory to solve differential equations. Many problems and solved exercises are included. Students are expected to gain a solid background and a versatile attitude towards calculus, algebra and geometry, which can be later used to acquire new skills in more advanced scientific disciplines, such as bioinformatics, process engineering, and finance. At the same time, instructors are provided with extensive information and inspiration for the preparation of their own courses.

Author : Jim DeFranza,Daniel Gagliardi
Publisher : Waveland Press
Page : 488 pages
File Size : 50,8 Mb
Release : 2015-01-23
Category : Mathematics
ISBN : 9781478628828

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Introduction to Linear Algebra with Applications by Jim DeFranza,Daniel Gagliardi Pdf

Over the last few decades, linear algebra has become more relevant than ever. Applications have increased not only in quantity but also in diversity, with linear systems being used to solve problems in chemistry, engineering, economics, nutrition, urban planning, and more. DeFranza and Gagliardi introduce students to the topic in a clear, engaging, and easy-to-follow manner. Topics are developed fully before moving on to the next through a series of natural connections. The result is a solid introduction to linear algebra for undergraduates’ first course.

Author : Trevor James Fletcher
Publisher : Unknown
Page : 292 pages
File Size : 54,6 Mb
Release : 1972
Category : Mathematics
ISBN : UOM:39015014358413

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Linear Algebra; Through Its Applications by Trevor James Fletcher Pdf

Author : Peter Benner,Matthias Bollhöfer,Daniel Kressner,Christian Mehl,Tatjana Stykel
Publisher : Springer
Page : 608 pages
File Size : 46,8 Mb
Release : 2015-05-09
Category : Mathematics
ISBN : 9783319152608

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Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory by Peter Benner,Matthias Bollhöfer,Daniel Kressner,Christian Mehl,Tatjana Stykel Pdf

This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on differential-algebraic equations, to which he together with Peter Kunkel made many groundbreaking contributions, are the topic of the chapters in Part III. Besides providing a scientific discussion of Volker Mehrmann's work and its impact on the development of several areas of applied mathematics, the individual chapters stand on their own as reference works for selected topics in the fields of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory.

Author : Leiba Rodman
Publisher : Princeton University Press
Page : 378 pages
File Size : 46,8 Mb
Release : 2014-08-24
Category : Mathematics
ISBN : 9780691161853

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Topics in Quaternion Linear Algebra by Leiba Rodman Pdf

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

Author : Leslie Hogben
Publisher : CRC Press
Page : 1838 pages
File Size : 52,6 Mb
Release : 2013-11-26
Category : Mathematics
ISBN : 9781466507296

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Handbook of Linear Algebra by Leslie Hogben Pdf

With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and

Author : Kenneth Kuttler
Publisher : The Saylor Foundation
Page : 503 pages
File Size : 45,7 Mb
Release : 2012-01-29
Category : Mathematics
ISBN : 8210379456XXX

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Linear Algebra: Theory and Applications by Kenneth Kuttler Pdf

This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however. I think that the subject of linear algebra is likely the most significant topic discussed in undergraduate mathematics courses. Part of the reason for this is its usefulness in unifying so many different topics. Linear algebra is essential in analysis, applied math, and even in theoretical mathematics. This is the point of view of this book, more than a presentation of linear algebra for its own sake. This is why there are numerous applications, some fairly unusual.

Author : Cornelis V. M. van der Mee
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 51,5 Mb
Release : 2008-09-27
Category : Mathematics
ISBN : 9783764387327

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Exponentially Dichotomous Operators and Applications by Cornelis V. M. van der Mee Pdf

In this monograph the natural evolution operators of autonomous first-order differential equations with exponential dichotomy on an arbitrary Banach space are studied in detail. Characterizations of these so-called exponentially dichotomous operators in terms of their resolvents and additive and multiplicative perturbation results are given. This is the first book at graduate level on autonomous first-order differential equations with exponential dichotomy in a Banach space.

Author : Harry Dym,Marinus A. Kaashoek,Peter Lancaster,Heinz Langer,Leonid Lerer
Publisher : Springer Science & Business Media
Page : 642 pages
File Size : 42,6 Mb
Release : 2012-02-01
Category : Mathematics
ISBN : 9783034802215

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A Panorama of Modern Operator Theory and Related Topics by Harry Dym,Marinus A. Kaashoek,Peter Lancaster,Heinz Langer,Leonid Lerer Pdf

This book is dedicated to the memory of Israel Gohberg (1928–2009) – one of the great mathematicians of our time – who inspired innumerable fellow mathematicians and directed many students. The volume reflects the wide spectrum of Gohberg’s mathematical interests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory.

Author : Jeanne Agnew,Robert C. Knapp
Publisher : Thomson Brooks/Cole
Page : 392 pages
File Size : 42,6 Mb
Release : 1983
Category : Mathematics
ISBN : PSU:000015888075

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Linear Algebra with Applications by Jeanne Agnew,Robert C. Knapp Pdf

Author : Harry Dym
Publisher : American Mathematical Soc.
Page : 568 pages
File Size : 40,5 Mb
Release : 2007
Category : Mathematics
ISBN : 082183813X

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Linear Algebra in Action by Harry Dym Pdf

Linear algebra permeates mathematics, perhaps more so than any other single subject. It plays an essential role in pure and applied mathematics, statistics, computer science, and many aspects of physics and engineering. This book conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that the author wishes he had been taught as a graduate student. Roughly the first third of the book covers the basic material of a first course in linear algebra. The remaining chapters are devoted to applications drawn from vector calculus, numerical analysis, control theory, complex analysis, convexity and functional analysis. In particular, fixed point theorems, extremal problems, matrix equations, zero location and eigenvalue location problems, and matrices with nonnegative entries are discussed. Appendices on useful facts from analysis and supplementary information from complex function theory are also provided for the convenience of the reader. The book is suitable as a text or supplementary reference for a variety of courses on linear algebra and its applications, as well as for self-study.