Background
Minc, Henryk was born on November 12, 1919 in Lodz, Poland. Son of Izrael and Haja (Zyngler) Minc.
( Written for advanced undergraduate students, this highl...)
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.
http://www.amazon.com/gp/product/048667102X/?tag=2022091-20
(This text/reference is the most up-to-date volume on nonn...)
This text/reference is the most up-to-date volume on nonnegative matrices in print and presents much material that was previously available only in research papers. It is the only book to cover the van der Waerden conjecture on permanents. There is also coverage of doubly stochastic matrices and inverse problems. The material has abundant connections to graph theory, incidence geometry, stochastic processes, functional analysis, and quadratic forms. Each chapter contains a comprehensive set of problems and a substantial list of references.
http://www.amazon.com/gp/product/0471839663/?tag=2022091-20
Minc, Henryk was born on November 12, 1919 in Lodz, Poland. Son of Izrael and Haja (Zyngler) Minc.
Master of Arts with honors, Edinburgh University, Scotland, 1955. Doctor of Philosophy, Edinburgh University, Scotland, 1959.
Teacher Morgan Academy, Dundee, Scotland, 1956-1958. Lecturer Dundee Technology College, Scotland, 1957-1958, U. British Columbia, Vancouver, Canada, 1958-1959, assistant professor, 1959-1960. Associate professor of University Florida, Gainesville, 1960-1963.
Visiting professor Technion Israel Institute Technology, Haifa, 1969-1980.
Professor University of California-Santa Barbara, 1963-1990, emeritus, 1990. Referee and reviewer for mathematics journals.
(This text/reference is the most up-to-date volume on nonn...)
( Written for advanced undergraduate students, this highl...)
Fellow Society Antiquaries of Scotland. Member American Mathematics Society, Robert Burns World Federation (honorary president), Institute Antiquity and Christianity, Scottish Society Santa Barbara (past chieftain), Scots Language Society, Saltire Society, Association for Scottish Literature Studies, James Hogg Society, Santa Barbara Elks Lodge, Clan Fraser Society North America.
Married Catherine Taylor Duncan, April 16, 1943. Children: Robert Henry, Ralph Edward, Raymond.