A Survey of Matrix Theory and Matrix Inequalities

Nonfiction, Science & Nature, Mathematics, Matrices
Cover of the book A Survey of Matrix Theory and Matrix Inequalities by Marvin Marcus, Henryk Minc, Dover Publications
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Marvin Marcus, Henryk Minc ISBN: 9780486153063
Publisher: Dover Publications Publication: May 5, 2014
Imprint: Dover Publications Language: English
Author: Marvin Marcus, Henryk Minc
ISBN: 9780486153063
Publisher: Dover Publications
Publication: May 5, 2014
Imprint: Dover Publications
Language: English

Written for advanced undergraduate students, this highly regarded book presents an enormous amount of information in a concise and accessible format. Beginning with the assumption that the reader has never seen a matrix before, the authors go on to provide a survey of a substantial part of the field, including many areas of modern research interest.
Part One of the book covers not only the standard ideas of matrix theory, but ones, as the authors state, "that reflect our own prejudices," among them Kronecker products, compound and induced matrices, quadratic relations, permanents, incidence matrices and generalizations of commutativity.
Part Two begins with a survey of elementary properties of convex sets and polyhedra and presents a proof of the Birkhoff theorem on doubly stochastic matrices. This is followed by a discussion of the properties of convex functions and a list of classical inequalities. This material is then combined to yield many of the interesting matrix inequalities of Weyl, Fan, Kantorovich and others. The treatment is along the lines developed by these authors and their successors and many of their proofs are included. This chapter contains an account of the classical Perron Frobenius-Wielandt theory of indecomposable nonnegative matrices and ends with some important results on stochastic matrices.
Part Three is concerned with a variety of results on the localization of the characteristic roots of a matrix in terms of simple functions of its entries or of entries of a related matrix. The presentation is essentially in historical order, and out of the vast number of results in this field the authors have culled those that seemed most interesting or useful. Readers will find many of the proofs of classical theorems and a substantial number of proofs of results in contemporary research literature.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

Written for advanced undergraduate students, this highly regarded book presents an enormous amount of information in a concise and accessible format. Beginning with the assumption that the reader has never seen a matrix before, the authors go on to provide a survey of a substantial part of the field, including many areas of modern research interest.
Part One of the book covers not only the standard ideas of matrix theory, but ones, as the authors state, "that reflect our own prejudices," among them Kronecker products, compound and induced matrices, quadratic relations, permanents, incidence matrices and generalizations of commutativity.
Part Two begins with a survey of elementary properties of convex sets and polyhedra and presents a proof of the Birkhoff theorem on doubly stochastic matrices. This is followed by a discussion of the properties of convex functions and a list of classical inequalities. This material is then combined to yield many of the interesting matrix inequalities of Weyl, Fan, Kantorovich and others. The treatment is along the lines developed by these authors and their successors and many of their proofs are included. This chapter contains an account of the classical Perron Frobenius-Wielandt theory of indecomposable nonnegative matrices and ends with some important results on stochastic matrices.
Part Three is concerned with a variety of results on the localization of the characteristic roots of a matrix in terms of simple functions of its entries or of entries of a related matrix. The presentation is essentially in historical order, and out of the vast number of results in this field the authors have culled those that seemed most interesting or useful. Readers will find many of the proofs of classical theorems and a substantial number of proofs of results in contemporary research literature.

More books from Dover Publications

Cover of the book Boolean Algebra and Its Applications by Marvin Marcus, Henryk Minc
Cover of the book Elements of Tensor Calculus by Marvin Marcus, Henryk Minc
Cover of the book Fundamentals of the Theory of Plasticity by Marvin Marcus, Henryk Minc
Cover of the book Botchan by Marvin Marcus, Henryk Minc
Cover of the book The Unknown Masterpiece and Other Stories by Marvin Marcus, Henryk Minc
Cover of the book Sister Carrie by Marvin Marcus, Henryk Minc
Cover of the book A Handbook of Weaves by Marvin Marcus, Henryk Minc
Cover of the book Introduction to Proof in Abstract Mathematics by Marvin Marcus, Henryk Minc
Cover of the book Singular Integral Equations by Marvin Marcus, Henryk Minc
Cover of the book Personal Recollections of Vincent Van Gogh by Marvin Marcus, Henryk Minc
Cover of the book A History of Japanese Mathematics by Marvin Marcus, Henryk Minc
Cover of the book Cautionary Tales & Bad Child's Book of Beasts by Marvin Marcus, Henryk Minc
Cover of the book Gilbert's Table Magic by Marvin Marcus, Henryk Minc
Cover of the book Cup and Saucer Chemistry by Marvin Marcus, Henryk Minc
Cover of the book King Lear Thrift Study Edition by Marvin Marcus, Henryk Minc
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy