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Linear Algebra And Matrix Theory

Author: Jimmie Gilbert
Publisher: Elsevier
ISBN: 0080510256
Size: 58.62 MB
Format: PDF, ePub, Mobi
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Intended for a serious first course or a second course, this textbook will carry students beyond eigenvalues and eigenvectors to the classification of bilinear forms, to normal matrices, to spectral decompositions, and to the Jordan form. The authors approach their subject in a comprehensive and accessible manner, presenting notation and terminology clearly and concisely, and providing smooth transitions between topics. The examples and exercises are well designed and will aid diligent students in understanding both computational and theoretical aspects. In all, the straightest, smoothest path to the heart of linear algebra. * Special Features: * Provides complete coverage of central material. * Presents clear and direct explanations. * Includes classroom tested material. * Bridges the gap from lower division to upper division work. * Allows instructors alternatives for introductory or second-level courses.

Linear Algebra And Matrix Theory

Author: Robert R. Stoll
Publisher: Courier Corporation
ISBN: 0486265218
Size: 45.42 MB
Format: PDF, ePub
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One of the best available works on matrix theory in the context of modern algebra, this text bridges the gap between ordinary undergraduate studies and completely abstract mathematics. 1952 edition.

Linear Algebra And Matrix Analysis For Statistics

Author: Sudipto Banerjee
Publisher: CRC Press
ISBN: 1420095382
Size: 24.71 MB
Format: PDF, Kindle
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Linear Algebra and Matrix Analysis for Statistics offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book is as self-contained as possible, assuming no prior knowledge of linear algebra. The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction. The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces.

Linear Algebra And Matrix Theory

Author: Evar D. Nering
Size: 66.27 MB
Format: PDF, Kindle
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Vector spaces; Linear transformations and matrices; Determinants, eigenvalues, and similarity transformations; Linear functionals, Bilinear forms, quadratic forms; Orthogonal and unitary transformations, normal matrices; Selected applications of linear algebra; Appendix; Index.

Linear Algebra And Matrices Topics For A Second Course

Author: Helene Shapiro
Publisher: American Mathematical Soc.
ISBN: 1470418525
Size: 55.79 MB
Format: PDF, ePub, Docs
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Linear algebra and matrix theory are fundamental tools for almost every area of mathematics, both pure and applied. This book combines coverage of core topics with an introduction to some areas in which linear algebra plays a key role, for example, block designs, directed graphs, error correcting codes, and linear dynamical systems. Notable features include a discussion of the Weyr characteristic and Weyr canonical forms, and their relationship to the better-known Jordan canonical form; the use of block cyclic matrices and directed graphs to prove Frobenius's theorem on the structure of the eigenvalues of a nonnegative, irreducible matrix; and the inclusion of such combinatorial topics as BIBDs, Hadamard matrices, and strongly regular graphs. Also included are McCoy's theorem about matrices with property P, the Bruck-Ryser-Chowla theorem on the existence of block designs, and an introduction to Markov chains. This book is intended for those who are familiar with the linear algebra covered in a typical first course and are interested in learning more advanced results.

Matrix Theory

Author: Fuzhen Zhang
Publisher: Springer Science & Business Media
ISBN: 1475757972
Size: 30.83 MB
Format: PDF, ePub
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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.

Elementary Matrix Theory

Author: Howard Eves
Publisher: Courier Corporation
ISBN: 0486150275
Size: 57.60 MB
Format: PDF, ePub, Docs
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Concrete treatment of fundamental concepts and operations, equivalence, determinants, matrices with polynomial elements, and similarity and congruence. Each chapter has many excellent problems and optional related information. No previous course in abstract algebra required.

Linear Algebra And Matrices

Author: Shmuel Friedland
Publisher: SIAM
ISBN: 161197514X
Size: 64.39 MB
Format: PDF, Docs
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This introductory textbook grew out of several courses in linear algebra given over more than a decade and includes such helpful material as constructive discussions about the motivation of fundamental concepts, many worked-out problems in each chapter, and topics rarely covered in typical linear algebra textbooks.The authors use abstract notions and arguments to give the complete proof of the Jordan canonical form and, more generally, the rational canonical form of square matrices over fields. They also provide the notion of tensor products of vector spaces and linear transformations. Matrices are treated in depth, with coverage of the stability of matrix iterations, the eigenvalue properties of linear transformations in inner product spaces, singular value decomposition, and min-max characterizations of Hermitian matrices and nonnegative irreducible matrices. The authors show the many topics and tools encompassed by modern linear algebra to emphasize its relationship to other areas of mathematics. The text is intended for advanced undergraduate students. Beginning graduate students seeking an introduction to the subject will also find it of interest.