Linear Operators And Matrices

Author : Israel Gohberg,Heinz Langer
Publisher : Birkhäuser
Page : 282 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034881814

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Linear Operators and Matrices by Israel Gohberg,Heinz Langer Pdf

In September 1998, during the 'International Workshop on Analysis and Vibrat ing Systems' held in Canmore, Alberta, Canada, it was decided by a group of participants to honour Peter Lancaster on the occasion of his 70th birthday with a volume in the series 'Operator Theory: Advances and Applications'. Friends and colleagues responded enthusiastically to this proposal and within a short time we put together the volume which is now presented to the reader. Regarding accep tance of papers we followed the usual rules of the journal 'Integral Equations and Operator Theory'. The papers are dedicated to different problems in matrix and operator theory, especially to the areas in which Peter contributed so richly. At our request, Peter agreed to write an autobiographical paper, which appears at the beginning of the volume. It continues with the list of Peter's publications. We believe that this volume will pay tribute to Peter on his outstanding achievements in different areas of mathematics. 1. Gohberg, H. Langer P ter Lancast r *1929 Operator Theory: Advances and Applications, Vol. 130, 1- 7 © 2001 Birkhiiuser Verlag Basel/Switzerland My Life and Mathematics Peter Lancaster I was born in Appleby, a small county town in the north of England, on November 14th, 1929. I had two older brothers and was to have one younger sister. My family moved around the north of England as my father's work in an insurance company required.

Author : Karl E. Gustafson,Duggirala K.M. Rao
Publisher : Springer Science & Business Media
Page : 202 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461384984

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Numerical Range by Karl E. Gustafson,Duggirala K.M. Rao Pdf

The theories of quadratic forms and their applications appear in many parts of mathematics and the sciences. All students of mathematics have the opportunity to encounter such concepts and applications in their first course in linear algebra. This subject and its extensions to infinite dimen sions comprise the theory of the numerical range W(T). There are two competing names for W(T), namely, the numerical range of T and the field of values for T. The former has been favored historically by the func tional analysis community, the latter by the matrix analysis community. It is a toss-up to decide which is preferable, and we have finally chosen the former because it is our habit, it is a more efficient expression, and because in recent conferences dedicated to W(T), even the linear algebra commu nity has adopted it. Also, one universally refers to the numerical radius, and not to the field of values radius. Originally, Toeplitz and Hausdorff called it the Wertvorrat of a bilinear form, so other good names would be value field or form values. The Russian community has referred to it as the Hausdorff domain. Murnaghan in his early paper first called it the region of the complex plane covered by those values for an n x n matrix T, then the range of values of a Hermitian matrix, then the field of values when he analyzed what he called the sought-for region.

Author : Takayuki Furuta
Publisher : CRC Press
Page : 276 pages
File Size : 54,6 Mb
Release : 2001-07-26
Category : Mathematics
ISBN : 0415267994

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Invitation to Linear Operators by Takayuki Furuta Pdf

Most books on linear operators are not easy to follow for students and researchers without an extensive background in mathematics. Self-contained and using only matrix theory, Invitation to Linear Operators: From Matricies to Bounded Linear Operators on a Hilbert Space explains in easy-to-follow steps a variety of interesting recent results on linear operators on a Hilbert space. The author first states the important properties of a Hilbert space, then sets out the fundamental properties of bounded linear operators on a Hilbert space. The final section presents some of the more recent developments in bounded linear operators.

Author : Aref Jeribi
Publisher : Springer
Page : 599 pages
File Size : 47,9 Mb
Release : 2015-07-04
Category : Science
ISBN : 9783319175669

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Spectral Theory and Applications of Linear Operators and Block Operator Matrices by Aref Jeribi Pdf

Examining recent mathematical developments in the study of Fredholm operators, spectral theory and block operator matrices, with a rigorous treatment of classical Riesz theory of polynomially-compact operators, this volume covers both abstract and applied developments in the study of spectral theory. These topics are intimately related to the stability of underlying physical systems and play a crucial role in many branches of mathematics as well as numerous interdisciplinary applications. By studying classical Riesz theory of polynomially compact operators in order to establish the existence results of the second kind operator equations, this volume will assist the reader working to describe the spectrum, multiplicities and localization of the eigenvalues of polynomially-compact operators.

Author : Francoise Chatelin
Publisher : SIAM
Page : 482 pages
File Size : 46,8 Mb
Release : 2011-05-26
Category : Mathematics
ISBN : 9780898719994

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Spectral Approximation of Linear Operators by Francoise Chatelin Pdf

Originally published: New York: Academic Press, 1983.

Author : Nita H. Shah,Urmila B. Chaudhari
Publisher : CRC Press
Page : 70 pages
File Size : 41,6 Mb
Release : 2020-12-29
Category : Mathematics
ISBN : 9781000337440

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Linear Transformation by Nita H. Shah,Urmila B. Chaudhari Pdf

This book introduces linear transformation and its key results, which have applications in engineering, physics, and various branches of mathematics. Linear transformation is a difficult subject for students. This concise text provides an in-depth overview of linear trans-formation. It provides multiple-choice questions, covers enough examples for the reader to gain a clear understanding, and includes exact methods with specific shortcuts to reach solutions for particular problems. Research scholars and students working in the fields of engineering, physics, and different branches of mathematics need to learn the concepts of linear transformation to solve their problems. This book will serve their need instead of having to use the more complex texts that contain more concepts then needed. The chapters mainly discuss the definition of linear transformation, properties of linear transformation, linear operators, composition of two or more linear transformations, kernels and range of linear transformation, inverse transformation, one-to-one and onto transformation, isomorphism, matrix linear transformation, and similarity of two matrices.

Author : I. Gohberg
Publisher : Birkhäuser
Page : 311 pages
File Size : 40,8 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783034877015

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Extension and Interpolation of Linear Operators and Matrix Functions by I. Gohberg Pdf

Author : Israel Gohberg,Seymour Goldberg,Nahum Krupnik
Publisher : Birkhäuser
Page : 261 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034884013

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Traces and Determinants of Linear Operators by Israel Gohberg,Seymour Goldberg,Nahum Krupnik Pdf

This book is dedicated to a theory of traces and determinants on embedded algebras of linear operators, where the trace and determinant are extended from finite rank operators by a limit process. The self-contained material should appeal to a wide group of mathematicians and engineers, and is suitable for teaching.

Author : Takayuki Furuta
Publisher : Unknown
Page : 254 pages
File Size : 40,9 Mb
Release : 2001
Category : Hilbert space
ISBN : 9056993569

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Invitation to Linear Operators by Takayuki Furuta Pdf

Author : Jiu Ding,Aihui Zhou
Publisher : World Scientific Publishing Company
Page : 364 pages
File Size : 50,8 Mb
Release : 2009-08-24
Category : Mathematics
ISBN : 9789813107434

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Nonnegative Matrices, Positive Operators, and Applications by Jiu Ding,Aihui Zhou Pdf

Nonnegative matrices and positive operators are widely applied in science, engineering, and technology. This book provides the basic theory and several typical modern science and engineering applications of nonnegative matrices and positive operators, including the fundamental theory, methods, numerical analysis, and applications in the Google search engine, computational molecular dynamics, and wireless communications. Unique features of this book include the combination of the theories of nonnegative matrices and positive operators as well as the emphasis on applications of nonnegative matrices in the numerical analysis of positive operators, such as Markov operators and Frobenius–Perron operators both of which play key roles in the statistical and stochastic studies of dynamical systems. It can be used as a textbook for an upper level undergraduate or beginning graduate course in advanced matrix theory and/or positive operators as well as for an advanced topics course in operator theory or ergodic theory. In addition, it serves as a good reference for researchers in mathematical sciences, physical sciences, and engineering.

Author : Sheldon Axler
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 49,6 Mb
Release : 1997-07-18
Category : Mathematics
ISBN : 0387982590

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Linear Algebra Done Right by Sheldon Axler Pdf

This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.

Author : Carlos André,M. Amélia Bastos,Alexei Yu. Karlovich,Bernd Silbermann,Ion Zaballa
Publisher : Birkhäuser
Page : 372 pages
File Size : 42,7 Mb
Release : 2018-08-22
Category : Mathematics
ISBN : 9783319724492

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Operator Theory, Operator Algebras, and Matrix Theory by Carlos André,M. Amélia Bastos,Alexei Yu. Karlovich,Bernd Silbermann,Ion Zaballa Pdf

This book consists of invited survey articles and research papers in the scientific areas of the “International Workshop on Operator Algebras, Operator Theory and Applications,” which was held in Lisbon in July 2016. Reflecting recent developments in the field of algebras of operators, operator theory and matrix theory, it particularly focuses on groupoid algebras and Fredholm conditions, algebras of approximation sequences, C* algebras of convolution type operators, index theorems, spectrum and numerical range of operators, extreme supercharacters of infinite groups, quantum dynamics and operator algebras, and inverse eigenvalue problems. Establishing bridges between the three related areas of operator algebras, operator theory, and matrix theory, the book is aimed at researchers and graduate students who use results from these areas.

Author : Peter Lancaster,Israel Gohberg,H. Langer
Publisher : Birkhauser
Page : 281 pages
File Size : 48,5 Mb
Release : 2002
Category : Mathematics
ISBN : 0817666559

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Linear Operators and Matrices by Peter Lancaster,Israel Gohberg,H. Langer Pdf

Author : Charles G. Cullen
Publisher : Courier Corporation
Page : 338 pages
File Size : 46,6 Mb
Release : 2012-09-20
Category : Mathematics
ISBN : 9780486132419

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Matrices and Linear Transformations by Charles G. Cullen Pdf

Undergraduate-level introduction to linear algebra and matrix theory. Explores matrices and linear systems, vector spaces, determinants, spectral decomposition, Jordan canonical form, much more. Over 375 problems. Selected answers. 1972 edition.

Author : Frederick P. Greenleaf,Sophie Marques
Publisher : American Mathematical Soc.
Page : 261 pages
File Size : 42,5 Mb
Release : 2019-01-30
Category : Algebras, Linear
ISBN : 9781470448714

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Linear Algebra I by Frederick P. Greenleaf,Sophie Marques Pdf

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.