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Author: Peter Lancaster
Publisher: Academic Press
ISBN: 9780124355606
Category : Computers
Languages : en
Pages : 590
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Book Description
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: Peter Lancaster
Publisher: Academic Press
ISBN: 9780124355606
Category : Computers
Languages : en
Pages : 590
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Book Description
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: Feliks Ruvimovich Gantmakher
Publisher:
ISBN:
Category : Matrices
Languages : en
Pages : 296
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Book Description
Author: Cyrus Colton MacDuffee
Publisher: Springer Science & Business Media
ISBN: 364299234X
Category : Mathematics
Languages : en
Pages : 121
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Book Description
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: Denis Serre
Publisher: Springer Science & Business Media
ISBN: 038722758X
Category : Mathematics
Languages : en
Pages : 215
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Book Description
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: Fuzhen Zhang
Publisher: Springer Science & Business Media
ISBN: 1475757972
Category : Mathematics
Languages : en
Pages : 290
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Book Description
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: Joel N. Franklin
Publisher: Courier Corporation
ISBN: 0486136388
Category : Mathematics
Languages : en
Pages : 319
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Book Description
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: F. R. Gantmacher
Publisher: Courier Corporation
ISBN: 0486445542
Category : Mathematics
Languages : en
Pages : 336
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Book Description
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: James M. Ortega
Publisher: Springer Science & Business Media
ISBN: 1489904719
Category : Mathematics
Languages : en
Pages : 269
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Book Description
Linear algebra and matrix theory are essentially synonymous terms for an area of mathematics that has become one of the most useful and pervasive tools in a wide range of disciplines. It is also a subject of great mathematical beauty. In consequence of both of these facts, linear algebra has increasingly been brought into lower levels of the curriculum, either in conjunction with the calculus or separate from it but at the same level. A large and still growing number of textbooks has been written to satisfy this need, aimed at students at the junior, sophomore, or even freshman levels. Thus, most students now obtaining a bachelor's degree in the sciences or engineering have had some exposure to linear algebra. But rarely, even when solid courses are taken at the junior or senior levels, do these students have an adequate working knowledge of the subject to be useful in graduate work or in research and development activities in government and industry. In particular, most elementary courses stop at the point of canonical forms, so that while the student may have "seen" the Jordan and other canonical forms, there is usually little appreciation of their usefulness. And there is almost never time in the elementary courses to deal with more specialized topics like nonnegative matrices, inertia theorems, and so on. In consequence, many graduate courses in mathematics, applied mathe matics, or applications develop certain parts of matrix theory as needed.
Author: Robert R. Stoll
Publisher: Courier Corporation
ISBN: 0486623181
Category : Mathematics
Languages : en
Pages : 290
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Book Description
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: Philip J. Davis
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 376
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Book Description
