Algebraic Multiplicity Of Eigenvalues Of Linear Operators

Author : Julián López-Gómez
Publisher : Springer Science & Business Media
ISBN 13 : 376438400X
Total Pages : 324 pages
Book Rating : 4.05/5 ( download)

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Download or read book Algebraic Multiplicity of Eigenvalues of Linear Operators written by Julián López-Gómez and published by Springer Science & Business Media. This book was released on 2007-06-22 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together all available results about the theory of algebraic multiplicities. It first offers a classic course on finite-dimensional spectral theory and then presents the most general results available about the existence and uniqueness of algebraic multiplicities for real non-analytic operator matrices and families. Coverage next transfers these results from linear to nonlinear analysis.

Author : Julián López-Gómez
Publisher : Springer Science & Business Media
ISBN 13 : 3764384018
Total Pages : 324 pages
Book Rating : 4.12/5 ( download)

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Download or read book Algebraic Multiplicity of Eigenvalues of Linear Operators written by Julián López-Gómez and published by Springer Science & Business Media. This book was released on 2007-08-09 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together all available results about the theory of algebraic multiplicities. It first offers a classic course on finite-dimensional spectral theory and then presents the most general results available about the existence and uniqueness of algebraic multiplicities for real non-analytic operator matrices and families. Coverage next transfers these results from linear to nonlinear analysis.

Author : Frederick P. Greenleaf
Publisher : American Mathematical Soc.
ISBN 13 : 1470448718
Total Pages : 261 pages
Book Rating : 4.14/5 ( download)

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Download or read book Linear Algebra I written by Frederick P. Greenleaf and published by American Mathematical Soc.. This book was released on 2019-01-30 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first of two volumes on linear algebra for graduate students in mathematics, the sciences, and economics, who have: a prior undergraduate course in the subject; a basic understanding of matrix algebra; and some proficiency with mathematical proofs. Proofs are emphasized and the overall objective is to understand the structure of linear operators as the key to solving problems in which they arise. This first volume re-examines basic notions of linear algebra: vector spaces, linear operators, duality, determinants, diagonalization, and inner product spaces, giving an overview of linear algebra with sufficient mathematical precision for advanced use of the subject. This book provides a nice and varied selection of exercises; examples are well-crafted and provide a clear understanding of the methods involved. New notions are well motivated and interdisciplinary connections are often provided, to give a more intuitive and complete vision of linear algebra. Computational aspects are fully covered, but the study of linear operators remains the focus of study in this book.

Author : Stephen Andrilli
Publisher : Academic Press
ISBN 13 : 9780080886251
Total Pages : 768 pages
Book Rating : 4.56/5 ( download)

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Download or read book Elementary Linear Algebra written by Stephen Andrilli and published by Academic Press. This book was released on 2010-02-04 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary Linear Algebra develops and explains in careful detail the computational techniques and fundamental theoretical results central to a first course in linear algebra. This highly acclaimed text focuses on developing the abstract thinking essential for further mathematical study The authors give early, intensive attention to the skills necessary to make students comfortable with mathematical proofs. The text builds a gradual and smooth transition from computational results to general theory of abstract vector spaces. It also provides flexbile coverage of practical applications, exploring a comprehensive range of topics. Ancillary list: * Maple Algorithmic testing- Maple TA- www.maplesoft.com Includes a wide variety of applications, technology tips and exercises, organized in chart format for easy reference More than 310 numbered examples in the text at least one for each new concept or application Exercise sets ordered by increasing difficulty, many with multiple parts for a total of more than 2135 questions Provides an early introduction to eigenvalues/eigenvectors A Student solutions manual, containing fully worked out solutions and instructors manual available

Author : Stephen Francis Andrilli
Publisher : Gulf Professional Publishing
ISBN 13 : 9780120586219
Total Pages : 696 pages
Book Rating : 4.15/5 ( download)

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Download or read book Elementary Linear Algebra written by Stephen Francis Andrilli and published by Gulf Professional Publishing. This book was released on 2003-10-31 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: The transition to upper-level math courses is often difficult because of the shift in emphasis from computation (in calculus) to abstraction and proof (in junior/senior courses). This book provides guidance with the reading and writing of short proofs, and incorporates a gradual increase in abstraction as the chapters progress. This helps students prepare to meet the challenges of future courses such as abstract algebra and elementary analysis. Clearly explains principles and guides students through the effective transition to higher-level math Includes a wide variety of applications, technology tips, and exercises, including new true/false exercises in every section Provides an early introduction to eigenvalues/eigenvectors Accompanying Instructor's Manual and Student Solutions Manual (ISBN: 0-12-058622-3)

Author : Tosio Kato
Publisher : Springer Science & Business Media
ISBN 13 : 146125700X
Total Pages : 172 pages
Book Rating : 4.04/5 ( download)

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Download or read book A Short Introduction to Perturbation Theory for Linear Operators written by Tosio Kato and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a slightly expanded reproduction of the first two chapters (plus Introduction) of my book Perturbation Theory tor Linear Operators, Grundlehren der mathematischen Wissenschaften 132, Springer 1980. Ever since, or even before, the publication of the latter, there have been suggestions about separating the first two chapters into a single volume. I have now agreed to follow the suggestions, hoping that it will make the book available to a wider audience. Those two chapters were intended from the outset to be a comprehen sive presentation of those parts of perturbation theory that can be treated without the topological complications of infinite-dimensional spaces. In fact, many essential and. even advanced results in the theory have non trivial contents in finite-dimensional spaces, although one should not forget that some parts of the theory, such as those pertaining to scatter ing. are peculiar to infinite dimensions. I hope that this book may also be used as an introduction to linear algebra. I believe that the analytic approach based on a systematic use of complex functions, by way of the resolvent theory, must have a strong appeal to students of analysis or applied mathematics, who are usually familiar with such analytic tools.

Author : Marat V. Markin
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110598884
Total Pages : 406 pages
Book Rating : 4.89/5 ( download)

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Download or read book Elementary Operator Theory written by Marat V. Markin and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-04-06 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is intended as a text for a one-semester graduate course in operator theory to be taught "from scratch'', not as a sequel to a functional analysis course, with the basics of the spectral theory of linear operators taking the center stage. The book consists of six chapters and appendix, with the material flowing from the fundamentals of abstract spaces (metric, vector, normed vector, and inner product), the Banach Fixed-Point Theorem and its applications, such as Picard's Existence and Uniqueness Theorem, through the basics of linear operators, two of the three fundamental principles (the Uniform Boundedness Principle and the Open Mapping Theorem and its equivalents: the Inverse Mapping and Closed Graph Theorems), to the elements of the spectral theory, including Gelfand's Spectral Radius Theorem and the Spectral Theorem for Compact Self-Adjoint Operators, and its applications, such as the celebrated Lyapunov Stability Theorem. Conceived as a text to be used in a classroom, the book constantly calls for the student's actively mastering the knowledge of the subject matter. There are problems at the end of each chapter, starting with Chapter 2 and totaling at 150. Many important statements are given as problems and frequently referred to in the main body. There are also 432 Exercises throughout the text, including Chapter 1 and the Appendix, which require of the student to prove or verify a statement or an example, fill in certain details in a proof, or provide an intermediate step or a counterexample. They are also an inherent part of the material. More difficult problems are marked with an asterisk, many problems and exercises are supplied with "existential'' hints. The book is generous on Examples and contains numerous Remarks accompanying definitions, examples, and statements to discuss certain subtleties, raise questions on whether the converse assertions are true, whenever appropriate, or whether the conditions are essential. With carefully chosen material, proper attention given to applications, and plenty of examples, problems, and exercises, this well-designed text is ideal for a one-semester Master's level graduate course in operator theory with emphasis on spectral theory for students majoring in mathematics, physics, computer science, and engineering. Contents Preface Preliminaries Metric Spaces Vector Spaces, Normed Vector Spaces, and Banach Spaces Linear Operators Elements of Spectral Theory in a Banach Space Setting Elements of Spectral Theory in a Hilbert Space Setting Appendix: The Axiom of Choice and Equivalents Bibliography Index

Author : Frederick P. Greenleaf
Publisher : American Mathematical Soc.
ISBN 13 : 1470454254
Total Pages : 288 pages
Book Rating : 4.58/5 ( download)

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Download or read book Linear Algebra II written by Frederick P. Greenleaf and published by American Mathematical Soc.. This book was released on 2020-05-06 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second of two volumes on linear algebra for graduate students in mathematics, the sciences, and economics, who have: a prior undergraduate course in the subject; a basic understanding of matrix algebra; and some proficiency with mathematical proofs. Both volumes have been used for several years in a one-year course sequence, Linear Algebra I and II, offered at New York University's Courant Institute. The first three chapters of this second volume round out the coverage of traditional linear algebra topics: generalized eigenspaces, further applications of Jordan form, as well as bilinear, quadratic, and multilinear forms. The final two chapters are different, being more or less self-contained accounts of special topics that explore more advanced aspects of modern algebra: tensor fields, manifolds, and vector calculus in Chapter 4 and matrix Lie groups in Chapter 5. The reader can choose to pursue either chapter. Both deal with vast topics in contemporary mathematics. They include historical commentary on how modern views evolved, as well as examples from geometry and the physical sciences in which these topics are important. The book provides a nice and varied selection of exercises; examples are well-crafted and provide a clear understanding of the methods involved.

Author : Saikia, Promode Kumar
Publisher : Pearson Education India
ISBN 13 : 8131742768
Total Pages : 461 pages
Book Rating : 4.61/5 ( download)

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Download or read book Linear Algebra: written by Saikia, Promode Kumar and published by Pearson Education India. This book was released on with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Algebra is designed for postgraduate and undergraduate students of Mathematics. This book explains the basics comprehensively and with clarity. The flowing narrative of the book provides a refreshing approach to the subject. Drawing on decad

Author : Stuart Antman
Publisher : Springer Science & Business Media
ISBN 13 : 1475741472
Total Pages : 762 pages
Book Rating : 4.76/5 ( download)

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Download or read book Nonlinear Problems of Elasticity written by Stuart Antman and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: The scientists of the seventeenth and eighteenth centuries, led by Jas. Bernoulli and Euler, created a coherent theory of the mechanics of strings and rods undergoing planar deformations. They introduced the basic con cepts of strain, both extensional and flexural, of contact force with its com ponents of tension and shear force, and of contact couple. They extended Newton's Law of Motion for a mass point to a law valid for any deformable body. Euler formulated its independent and much subtler complement, the Angular Momentum Principle. (Euler also gave effective variational characterizations of the governing equations. ) These scientists breathed life into the theory by proposing, formulating, and solving the problems of the suspension bridge, the catenary, the velaria, the elastica, and the small transverse vibrations of an elastic string. (The level of difficulty of some of these problems is such that even today their descriptions are sel dom vouchsafed to undergraduates. The realization that such profound and beautiful results could be deduced by mathematical reasoning from fundamental physical principles furnished a significant contribution to the intellectual climate of the Age of Reason. ) At first, those who solved these problems did not distinguish between linear and nonlinear equations, and so were not intimidated by the latter. By the middle of the nineteenth century, Cauchy had constructed the basic framework of three-dimensional continuum mechanics on the founda tions built by his eighteenth-century predecessors.