Matrix Theory And Applications

Author : Denis Serre
Publisher : Springer Science & Business Media
ISBN 13 : 1441976833
Total Pages : 291 pages
Book Rating : 4.33/5 ( download)

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Download or read book Matrices written by Denis Serre and published by Springer Science & Business Media. This book was released on 2010-10-26 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Karl Blum
Publisher : Springer Science & Business Media
ISBN 13 : 1461568080
Total Pages : 217 pages
Book Rating : 4.87/5 ( download)

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Download or read book Density Matrix Theory and Applications written by Karl Blum and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Alexander Graham
Publisher : Courier Dover Publications
ISBN 13 : 0486832651
Total Pages : 304 pages
Book Rating : 4.54/5 ( download)

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Download or read book Matrix Theory and Applications for Scientists and Engineers written by Alexander Graham and published by Courier Dover Publications. This book was released on 2018-07-18 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this comprehensive text on matrix theory and its applications, Graham explores the underlying principles as well as the numerous applications of the various concepts presented. Includes numerous problems with solutions. 1979 edition.

Author : Richard A. Brualdi
Publisher : CRC Press
ISBN 13 : 9781420082241
Total Pages : 288 pages
Book Rating : 4.48/5 ( download)

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Download or read book A Combinatorial Approach to Matrix Theory and Its Applications written by Richard A. Brualdi and published by CRC Press. This book was released on 2008-08-06 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Charles R. Johnson
Publisher : American Mathematical Soc.
ISBN 13 : 0821801546
Total Pages : 272 pages
Book Rating : 4.43/5 ( download)

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Download or read book Matrix Theory and Applications written by Charles R. Johnson and published by American Mathematical Soc.. This book was released on 1990 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the lecture notes prepared for the AMS Short Course on Matrix Theory and Applications, held in Phoenix in January, 1989. Matrix theory continues to enjoy a renaissance that has accelerated in the past decade, in part because of stimulation from a variety of applications and considerable interplay with other parts of mathematics. In addition, the great increase in the number and vitality of specialists in the field has dispelled the popular misconception that the subject has been fully researched.

Author : James E. Gentle
Publisher : Springer Science & Business Media
ISBN 13 : 0387708723
Total Pages : 536 pages
Book Rating : 4.20/5 ( download)

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Download or read book Matrix Algebra written by James E. Gentle and published by Springer Science & Business Media. This book was released on 2007-07-27 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : A. R. Meenakshi
Publisher : MJP Publisher
ISBN 13 :
Total Pages : 310 pages
Book Rating : 4./5 ( download)

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Download or read book Fuzzy Matrix written by A. R. Meenakshi and published by MJP Publisher. This book was released on 2019-06-11 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to introduce fuzzy matrix theory as a basic framework for characterizing the full scope of the fuzzy sets concept and its relationship with the increasingly important concept of information and complexity in various sciences and professions. The book provides a wide coverage on the theoretical developments of fuzzy matrices and fuzzy vector spaces, on the theory of generalized inverses for fuzzy matrices, on fuzzy relations and on partial orderings on fuzzy matrices. The book also discusses the role of fuzzy matrices in the spectral theory of linear transformations on finite dimensional vector spaces. The concept of fuzzy matrix and its applications in document retrieval system, medical diagnosis, database management system, decision making theory and dynamical systems are developediteratively and illustrated with suitable examples wherever necessary. Each chapter has brief notes and exercises for the benefit of students.

Author : Hassan Yasser
Publisher : BoD – Books on Demand
ISBN 13 : 1789234662
Total Pages : 98 pages
Book Rating : 4.64/5 ( download)

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Download or read book Matrix Theory written by Hassan Yasser and published by BoD – Books on Demand. This book was released on 2018-08-29 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews current research, including applications of matrices, spaces, and other characteristics. It discusses the application of matrices, which has become an area of great importance in many scientific fields. The theory of row/column determinants of a partial solution to the system of two-sided quaternion matrix equations is analyzed. It introduces a matrix that has the exponential function as one of its eigenvectors and realizes that this matrix represents finite difference derivation of vectors on a partition. Mixing problems and the corresponding associated matrices have different structures that deserve to be studied in depth. Special compound magic squares will be considered. Finally, a new type of regular matrix generated by Fibonacci numbers is introduced and we shall investigate its various topological properties.

Author : F. R. Gantmacher
Publisher : Courier Corporation
ISBN 13 : 0486445542
Total Pages : 336 pages
Book Rating : 4.40/5 ( download)

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Download or read book Applications of the Theory of Matrices written by F. R. Gantmacher and published by Courier Corporation. This book was released on 2005-01-01 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Denis Serre
Publisher : Springer Science & Business Media
ISBN 13 : 038722758X
Total Pages : 215 pages
Book Rating : 4.80/5 ( download)

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Download or read book Matrices written by Denis Serre and published by Springer Science & Business Media. This book was released on 2007-12-18 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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