Applications Of The Theory Of Matrices PDF Download
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Author | : F. R. Gantmacher |
Publisher | : Courier Corporation |
Total Pages | : 336 |
Release | : 2005-01-01 |
Genre | : Mathematics |
ISBN | : 0486445542 |
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The breadth of matrix theory's applications is reflected by this volume, which features material of interest to applied mathematicians as well as to control engineers studying stability of a servo-mechanism and numerical analysts evaluating the roots of a polynomial. Starting with a survey of complex symmetric, antisymmetric, and orthogonal matrices, the text advances to explorations of singular bundles of matrices and matrices with nonnegative elements. Applied mathematicians will take particular note of the full and readable chapter on applications of matrix theory to the study of systems of linear differential equations, and the text concludes with an exposition on the Routh-Hurwitz problem plus several helpful appendixes. 1959 edition.
Author | : Peter Lancaster |
Publisher | : Academic Press |
Total Pages | : 590 |
Release | : 1985-05-28 |
Genre | : Computers |
ISBN | : 9780124355606 |
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Matrix algebra; Determinants, inverse matrices, and rank; Linear, euclidean, and unitary spaces; Linear transformations and matrices; Linear transformations in unitary spaces and simple matrices; The jordan canonical form: a geometric approach; Matrix polynomials and normal forms; The variational method; Functions of matrices; Norms and bounds for eigenvalues; Perturbation theory; Linear matrices equations and generalized inverses; Stability problems; Matrix polynomials; Nonnegative matrices.
Author | : Denis Serre |
Publisher | : Springer Science & Business Media |
Total Pages | : 291 |
Release | : 2010-10-26 |
Genre | : Mathematics |
ISBN | : 1441976833 |
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In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: • Dunford decomposition, • tensor and exterior calculus, polynomial identities, • regularity of eigenvalues for complex matrices, • functional calculus and the Dunford–Taylor formula, • numerical range, • Weyl's and von Neumann’s inequalities, and • Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the École Normale Supérieure de Lyon.
Author | : Jason J. Molitierno |
Publisher | : CRC Press |
Total Pages | : 425 |
Release | : 2016-04-19 |
Genre | : Computers |
ISBN | : 1439863393 |
Download Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs Book in PDF, ePub and Kindle
On the surface, matrix theory and graph theory seem like very different branches of mathematics. However, adjacency, Laplacian, and incidence matrices are commonly used to represent graphs, and many properties of matrices can give us useful information about the structure of graphs.Applications of Combinatorial Matrix Theory to Laplacian Matrices o
Author | : Denis Serre |
Publisher | : Springer Science & Business Media |
Total Pages | : 215 |
Release | : 2007-12-18 |
Genre | : Mathematics |
ISBN | : 038722758X |
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Clear and concise introduction to matrices with elegant proofs; Of interest to scientists from many disciplines; Gives many interesting applications to different parts of mathematics, such as algebra, analysis and complexity theory; Contains 160 exercises, half of them on advanced material; Includes at least one advanced result per chapter
Author | : Peter Lancaster |
Publisher | : Elsevier |
Total Pages | : 589 |
Release | : 1985-05-24 |
Genre | : Mathematics |
ISBN | : 0080519083 |
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In this book the authors try to bridge the gap between the treatments of matrix theory and linear algebra. It is aimed at graduate and advanced undergraduate students seeking a foundation in mathematics, computer science, or engineering. It will also be useful as a reference book for those working on matrices and linear algebra for use in their scientific work.
Author | : R. B. Bapat |
Publisher | : Cambridge University Press |
Total Pages | : 351 |
Release | : 1997-03-28 |
Genre | : Mathematics |
ISBN | : 0521571677 |
Download Nonnegative Matrices and Applications Book in PDF, ePub and Kindle
This book provides an integrated treatment of the theory of nonnegative matrices (matrices with only positive numbers or zero as entries) and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimisation and mathematical economics. The wide variety of applications, which include price fixing, scheduling and the fair division problem, have been carefully chosen both for their elegant mathematical content and for their accessibility to students with minimal preparation. Many results in matrix theory are also presented. The treatment is rigorous and almost all results are proved completely. These results and applications will be of great interest to researchers in linear programming, statistics and operations research. The minimal prerequisites also make the book accessible to first-year graduate students.
Author | : Richard A. Brualdi |
Publisher | : CRC Press |
Total Pages | : 288 |
Release | : 2008-08-06 |
Genre | : Mathematics |
ISBN | : 9781420082241 |
Download A Combinatorial Approach to Matrix Theory and Its Applications Book in PDF, ePub and Kindle
Unlike most elementary books on matrices, A Combinatorial Approach to Matrix Theory and Its Applications employs combinatorial and graph-theoretical tools to develop basic theorems of matrix theory, shedding new light on the subject by exploring the connections of these tools to matrices. After reviewing the basics of graph theory, elementary counting formulas, fields, and vector spaces, the book explains the algebra of matrices and uses the König digraph to carry out simple matrix operations. It then discusses matrix powers, provides a graph-theoretical definition of the determinant using the Coates digraph of a matrix, and presents a graph-theoretical interpretation of matrix inverses. The authors develop the elementary theory of solutions of systems of linear equations and show how to use the Coates digraph to solve a linear system. They also explore the eigenvalues, eigenvectors, and characteristic polynomial of a matrix; examine the important properties of nonnegative matrices that are part of the Perron–Frobenius theory; and study eigenvalue inclusion regions and sign-nonsingular matrices. The final chapter presents applications to electrical engineering, physics, and chemistry. Using combinatorial and graph-theoretical tools, this book enables a solid understanding of the fundamentals of matrix theory and its application to scientific areas.
Author | : James E. Gentle |
Publisher | : Springer Science & Business Media |
Total Pages | : 536 |
Release | : 2007-07-27 |
Genre | : Computers |
ISBN | : 0387708723 |
Download Matrix Algebra Book in PDF, ePub and Kindle
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.
Author | : Karl Blum |
Publisher | : Springer Science & Business Media |
Total Pages | : 217 |
Release | : 2013-06-29 |
Genre | : Science |
ISBN | : 1461568080 |
Download Density Matrix Theory and Applications Book in PDF, ePub and Kindle
Quantum mechanics has been mostly concerned with those states of systems that are represented by state vectors. In many cases, however, the system of interest is incompletely determined; for example, it may have no more than a certain probability of being in the precisely defined dynamical state characterized by a state vector. Because of this incomplete knowledge, a need for statistical averaging arises in the same sense as in classical physics. The density matrix was introduced by J. von Neumann in 1927 to describe statistical concepts in quantum mechanics. The main virtue of the density matrix is its analytical power in the construction of general formulas and in the proof of general theorems. The evaluation of averages and probabilities of the physical quantities characterizing a given system is extremely cumbersome without the use of density matrix techniques. The representation of quantum mechanical states by density matrices enables the maximum information available on the system to be expressed in a compact manner and hence avoids the introduction of unnecessary vari ables. The use of density matrix methods also has the advantage of providing a uniform treatment of all quantum mechanical states, whether they are completely or incom~'\etely known. Until recently the use of the density matrix method has been mainly restricted to statistical physics. In recent years, however, the application of the density matrix has been gaining more and more importance in many other fields of physics.