The Theory Of Matrices
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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 | : Fuzhen Zhang |
Publisher | : Springer Science & Business Media |
Total Pages | : 290 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 1475757972 |
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This volume concisely presents fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and representative, followed by carefully selected problems. For many theorems several different proofs are given. The only prerequisites are a decent background in elementary linear algebra and calculus.
Author | : Feliks Ruvimovich Gantmakher |
Publisher | : American Mathematical Soc. |
Total Pages | : 276 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9780821826645 |
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This is an excellent and unusual textbook on the application of the theory of matrices. ... The text includes many chapters of interest to applied mathematicians. --Zentralblatt MATH This book is part of a two-volume set (the first volume is published by the AMS as volume 131 in the same series). Written by one of Russia's leading mathematicians, this treatise provides us, in easily accessible form, a coherent account of matrix theory with a view toward applications in mathematics, theoretical physics, statistics, electrical engineering, etc. The individual chapters have been kept as far as possible independent of each other, so that the reader acquainted with the contents of Chapter 1 of the first volume can proceed immediately to chapters of special interest. In this volume the reader will find the study of singular pencils of matrices, properties of matrices with nonnegative elements, applications to systems of linear differential equations, and the study of the Routh-Hurwitz problem and related questions.
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 | : Cyrus Colton MacDuffee |
Publisher | : Springer Science & Business Media |
Total Pages | : 121 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 364299234X |
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Matric algebra is a mathematical abstraction underlying many seemingly diverse theories. Thus bilinear and quadratic forms, linear associative algebra (hypercomplex systems), linear homogeneous trans formations and linear vector functions are various manifestations of matric algebra. Other branches of mathematics as number theory, differential and integral equations, continued fractions, projective geometry etc. make use of certain portions of this subject. Indeed, many of the fundamental properties of matrices were first discovered in the notation of a particular application, and not until much later re cognized in their generality. It was not possible within the scope of this book to give a completely detailed account of matric theory, nor is it intended to make it an authoritative history of the subject. It has been the desire of the writer to point out the various directions in which the theory leads so that the reader may in a general way see its extent. While some attempt has been made to unify certain parts of the theory, in general the material has been taken as it was found in the literature, the topics discussed in detail being those in which extensive research has taken place. For most of the important theorems a brief and elegant proof has sooner or later been found. It is hoped that most of these have been incorporated in the text, and that the reader will derive as much plea sure from reading them as did the writer.
Author | : Joel N. Franklin |
Publisher | : Courier Corporation |
Total Pages | : 319 |
Release | : 2012-07-31 |
Genre | : Mathematics |
ISBN | : 0486136388 |
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Mathematically rigorous introduction covers vector and matrix norms, the condition-number of a matrix, positive and irreducible matrices, much more. Only elementary algebra and calculus required. Includes problem-solving exercises. 1968 edition.
Author | : Marvin Marcus |
Publisher | : Courier Corporation |
Total Pages | : 212 |
Release | : 1992-01-01 |
Genre | : Mathematics |
ISBN | : 9780486671024 |
Download A Survey of Matrix Theory and Matrix Inequalities Book in PDF, Epub and Kindle
Concise, masterly survey of a substantial part of modern matrix theory introduces broad range of ideas involving both matrix theory and matrix inequalities. Also, convexity and matrices, localization of characteristic roots, proofs of classical theorems and results in contemporary research literature, more. Undergraduate-level. 1969 edition. Bibliography.
Author | : Robert R. Stoll |
Publisher | : Courier Corporation |
Total Pages | : 290 |
Release | : 2012-10-17 |
Genre | : Mathematics |
ISBN | : 0486623181 |
Download Linear Algebra and Matrix Theory Book in PDF, Epub and Kindle
Advanced undergraduate and first-year graduate students have long regarded this text as one of the best available works on matrix theory in the context of modern algebra. Teachers and students will find it particularly suited to bridging the gap between ordinary undergraduate mathematics and completely abstract mathematics. The first five chapters treat topics important to economics, psychology, statistics, physics, and mathematics. Subjects include equivalence relations for matrixes, postulational approaches to determinants, and bilinear, quadratic, and Hermitian forms in their natural settings. The final chapters apply chiefly to students of engineering, physics, and advanced mathematics. They explore groups and rings, canonical forms for matrixes with respect to similarity via representations of linear transformations, and unitary and Euclidean vector spaces. Numerous examples appear throughout the text.
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 | : Edward Tankard Browne |
Publisher | : UNC Press Books |
Total Pages | : 310 |
Release | : 2018-08-25 |
Genre | : Mathematics |
ISBN | : 1469643901 |
Download Introduction to the Theory of Determinants and Matrices Book in PDF, Epub and Kindle
This text and reference book for mathematics students and for many people working in the social sciences contains in one volume the most important properties of matrices and determinants whose elements are real or complex numbers. The theory is developed from the classical point of view of Bocher, Wedderburn, MacDuffee, and Erobernus. Originally published in 1958. A UNC Press Enduring Edition -- UNC Press Enduring Editions use the latest in digital technology to make available again books from our distinguished backlist that were previously out of print. These editions are published unaltered from the original, and are presented in affordable paperback formats, bringing readers both historical and cultural value.