 
Summary: Department of Mathematics & Statistics
GRADUATE STUDENT SEMINAR
Speaker: Yongjun Xing
Title: On the Spread of Real Symmetric Matrices with Entries in an Interval
Date: Thursday, November 29, 2007
Time: 1.30 pm
Location: College West 307.20
Abstract: The spread of a matrix has extensive and practical applications in combina
torial optimization problems and cybernetics problems. There are many papers on the
spread of a symmetric matrix, but restricting the entries of such n n symmetric matrices
to each lie in OE a; b seems to be a new view of this problem. As a first step, we show
that the entries must equal a or b in the case when the spread is maximum. Next, when
the spread attains the upper bound of Mirsky's seminal result, we describe the structure
of those matrices. Then we focus our study on the maximal value of the spread and the
corresponding structure of the matrix that achieves the maximum spread over all real sym
metric, n n matrices, whose entries lie in a given interval. Matlab is used as a tool to
aid the verification of some cases.
Supervisor: S Fallat
Coffee & cookies will be served in the Lounge prior to the lecture
