A Survey Of Matrix Theory And Matrix Inequalities Marvin Marcus(Allyn And Bacon 1964 197S).pdf

A SURVEY OF
MATRIX THEORY
AND
MATRIX INEQUALITIES
MARVIN MARCUS
HENRY* MINC
University of California, Santa Barbara
ALLYN AND BACON. INC,. BOSTON. 1964
THIS BOOK IS PART OF THE ALLYN AND BACON SERIES IN ADVANCED MATH-
EHATIa, CONSULTINO EDITOR, IRVING KAPLANSKY, UNIVERSITY OF CHICAGO.
Copyrleht @ 1964 by Allyn and Bacon, Inc., 1 SO Tremont Street,
Burton, All right8 rercrvcd, No part of this book may be reproduced
In any form, by mimeograph or any other means, without permission
in writing from the publihers.
Library of Cong~ssCotdoj Card Numbn: 64-14269,
Prlntad in the Udtad Sum of America.
To Arlen and Catherine
Preface
MODERNMATRIX THEORY is a subject that has lately gained considerable
popularity both as a suitable topic for undergraduate students and as an
interesting area for mathematical research. Apart from aesthetic reasons
this is a result of the widespread use of matrices in both pure mathematics
and the physical and social sciences.
In this book we have tried within relatively few pages to provide a
survey of a substantial part of the field. The first chapter starts with the
assumption that the reader has never seen a matrix before, and then leads
within a short space to many ideas which are of current research interest.
In order to plish this within limited space, certain proofs that can
be found in any of a very considerable list of books have been left out.
However, we have included many of the proofs of classical theorems as
well as a substantial number of proofs of results that are in the current
research literature. We have found that a subset of the material covered
in Chapter I is ample for a one-year course at the third- or fourth-year
undergraduate level. Of course, the instructor must provide some proofs
but this is in accordance with our own personal preference not to regurgi-
tate "definition-theorem-proof" from the printed page. There are many
idem covered in