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Author | : Denis Serre |
Publisher | : Springer Science & Business Media |
Total Pages | : 291 |
Release | : 2010-10-26 |
Genre | : Mathematics |
ISBN | : 1441976833 |
Download Matrices Book in PDF, ePub and Kindle
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 |
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.
Author | : F. R. Gantmacher |
Publisher | : Courier Corporation |
Total Pages | : 336 |
Release | : 2005-01-01 |
Genre | : Mathematics |
ISBN | : 0486445542 |
Download Applications of the Theory of Matrices Book in PDF, ePub and Kindle
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 |
Total Pages | : 215 |
Release | : 2007-12-18 |
Genre | : Mathematics |
ISBN | : 038722758X |
Download Matrices Book in PDF, ePub and Kindle
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 | : Alexander Graham |
Publisher | : Courier Dover Publications |
Total Pages | : 304 |
Release | : 2018-07-18 |
Genre | : Mathematics |
ISBN | : 0486832651 |
Download Matrix Theory and Applications for Scientists and Engineers Book in PDF, ePub and Kindle
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 | : Xian-Da Zhang |
Publisher | : Cambridge University Press |
Total Pages | : 761 |
Release | : 2017-10-05 |
Genre | : Computers |
ISBN | : 1108417418 |
Download Matrix Analysis and Applications Book in PDF, ePub and Kindle
The theory, methods and applications of matrix analysis are presented here in a novel theoretical framework.
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 | : Peter Lancaster |
Publisher | : Academic Press |
Total Pages | : 590 |
Release | : 1985-05-28 |
Genre | : Computers |
ISBN | : 9780124355606 |
Download The Theory of Matrices Book in PDF, ePub and Kindle
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 | : Charles R. Johnson |
Publisher | : American Mathematical Soc. |
Total Pages | : 272 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : 0821801546 |
Download Matrix Theory and Applications Book in PDF, ePub and Kindle
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 | : Fumio Hiai |
Publisher | : Springer Science & Business Media |
Total Pages | : 337 |
Release | : 2014-02-06 |
Genre | : Mathematics |
ISBN | : 3319041509 |
Download Introduction to Matrix Analysis and Applications Book in PDF, ePub and Kindle
Matrices can be studied in different ways. They are a linear algebraic structure and have a topological/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis. This book explains these aspects of matrix analysis from a functional analysis point of view. After an introduction to matrices and functional analysis, it covers more advanced topics such as matrix monotone functions, matrix means, majorization and entropies. Several applications to quantum information are also included. Introduction to Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics.