Matrix Pencils

Matrix Pencils

Preface A conference devoted to Matrix Pencils was held March 22–24, 1982 at Hotel Larus, Pite Havsbad in Northern Sweden. It was organized jointly by the Institute of Information Processing, Numerical Analysis department at the ...

Author: B. Kagström

Publisher: Springer

ISBN: 9783540394471

Category: Mathematics

Page: 297

View: 360

Categories: Mathematics

Modelling and Control of Dynamical Systems Numerical Implementation in a Behavioral Framework

Modelling and Control of Dynamical Systems  Numerical Implementation in a Behavioral Framework

In fact in this way we can build a pencil of many mathematical structures and a pencil of matrices is not an exception. Matrix pencils arise in the study of linear continuous and discrete time invariant state space systems and ...

Author: Ricardo Zavala Yoe

Publisher: Springer

ISBN: 9783540787358

Category: Computers

Page: 154

View: 458

The Behavioral Approach for systems and control deals directly with the solution of the differential equations which represent the system. This book reviews this approach and offers new theoretic results. The programs and algorithms are MATLAB based.
Categories: Computers

Structured Matrices in Numerical Linear Algebra

Structured Matrices in Numerical Linear Algebra

Our goal is to provide a canonical expression, up to permutation, for companion pencils in this family, resembling the one provided in [17] for companion matrices, and to determine, up to permutation as well, how many different sparse ...

Author: Dario Andrea Bini

Publisher: Springer

ISBN: 9783030040888

Category: Mathematics

Page: 322

View: 103

This book gathers selected contributions presented at the INdAM Meeting Structured Matrices in Numerical Linear Algebra: Analysis, Algorithms and Applications, held in Cortona, Italy on September 4-8, 2017. Highlights cutting-edge research on Structured Matrix Analysis, it covers theoretical issues, computational aspects, and applications alike. The contributions, written by authors from the foremost international groups in the community, trace the main research lines and treat the main problems of current interest in this field. The book offers a valuable resource for all scholars who are interested in this topic, including researchers, PhD students and post-docs.
Categories: Mathematics

Topics in Quaternion Linear Algebra

Topics in Quaternion Linear Algebra

Chapter Eleven Matrix pencils with symmetries: Nonstandard involution In this chapter the subject matter involves quaternion matrix pencils or, equiva— lently, pairs of quaternion matrices, with symmetries with respect to a fixed ...

Author: Leiba Rodman

Publisher: Princeton University Press

ISBN: 9781400852741

Category: Mathematics

Page: 384

View: 882

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.
Categories: Mathematics

Introduction to the Spectral Theory of Polynomial Operator Pencils

Introduction to the Spectral Theory of Polynomial Operator Pencils

If any 2 x 2 matrix pencil L(A) satisfying the condition (L(A)f f) #0 (A e T, f # 0) (27.13) has a spectral divisor whose spectrum coincides with a (L) O G+, then T is a circle. PROOF. In view of Theorem 27.5 it suffices to show that ...

Author: A. S. Markus

Publisher: American Mathematical Soc.

ISBN: 9780821890820

Category: Polynomial operator pencils

Page: 250

View: 857

This monograph contains an exposition of the foundations of the spectral theory of polynomial operator pencils acting in a Hilbert space. Spectral problems for polynomial pencils have attracted a steady interest in the last 35 years, mainly because they arise naturally in such diverse areas of mathematical physics as differential equations and boundary value problems, controllable systems, the theory of oscillations and waves, elasticity theory, and hydromechanics. In this book, the author devotes most of his attention to the fundamental results of Keldysh on multiple completeness of the eigenvectors and associate vectors of a pencil, and on the asymptotic behavior of its eigenvalues and generalizations of these results. The author also presents various theorems on spectral factorization of pencils which grew out of known results of M. G. Krein and Heinz Langer. A large portion of the book involves the theory of selfadjoint pencils, an area having numerous applications. Intended for mathematicians, researchers in mechanics, and theoretical physicists interested in spectral theory and its applications, the book assumes a familiarity with the fundamentals of spectral theory of operators acting in a Hilbert space.
Categories: Polynomial operator pencils

Differential algebraic Systems and Matrix Pencils

Differential algebraic Systems and Matrix Pencils

can be completely understood via the Kronecker canonical form of the matrix pencil ( A , B ) . The important characteristic of equation ( 4 ) that determines the behavior of the system and numerical methods is the nilpotency of the ...

Author: Charles William Gear

Publisher:

ISBN: UIUC:30112121952235

Category: Differential algebra

Page: 27

View: 886

Categories: Differential algebra

Matrix Computations

Matrix Computations

“The Set of 2-by-3 Matrix Pencils — Kronecker Structures and Their Transitions under Perturbations,” SIAM J. Matrix Anal. Applic. 17, 1–34. A. Edelman, E. Elmroth, and B. Kågström (1997). “A Geometric Approach to Perturbation Theory of ...

Author: Gene H. Golub

Publisher: JHU Press

ISBN: 9781421408590

Category: Mathematics

Page: 784

View: 423

The second most cited math book of 2012 according to MathSciNet, the book has placed in the top 10 for since 2005.
Categories: Mathematics

System Theory the Schur Algorithm and Multidimensional Analysis

System Theory  the Schur Algorithm and Multidimensional Analysis

0 X Now the uniqueness of the Kronecker canonical form Over C for the complex matrix pencil Ötijk} c(A0)+tö(i,j,k} c(Bo) (see, ... Canonical forms for symmetric matrix pencils We fix a nonstandard iaa () throughout Subsection 7.1.

Author: Daniel Alpay

Publisher: Springer Science & Business Media

ISBN: 9783764381370

Category: Mathematics

Page: 322

View: 184

This volume contains six peer-refereed articles written on the occasion of the workshop Operator theory, system theory and scattering theory: multidimensional generalizations and related topics, held at the Department of Mathematics of the Ben-Gurion University of the Negev in June, 2005. The book will interest a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.
Categories: Mathematics

Numerical Methods in Matrix Computations

Numerical Methods in Matrix Computations

Definition 3.7.1 Let (A, B) be a matrix pencil and let S and T be nonsingular matrices. Then the two matrix pencils A − λB and SAT − λSBT are said to be equivalent. Equivalent pencils have the same characteristic equation and hence ...

Author: Åke Björck

Publisher: Springer

ISBN: 9783319050898

Category: Mathematics

Page: 800

View: 260

Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.
Categories: Mathematics

Matrix Algebra

Matrix Algebra

3.8.12.1 Matrix Pencils As c ranges over the reals (or, more generally, the complex numbers), the set of matrices of the form A − cB is called the matrix pencil, or just the pencil, generated by A and B, denoted as (A, B).

Author: James E. Gentle

Publisher: Springer

ISBN: 9783319648675

Category: Mathematics

Page: 648

View: 671

Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.
Categories: Mathematics