 
Summary: Department of Mathematics & Statistics
GRADUATE STUDENT SEMINAR
Speaker: Michael S. Cavers
Title: Reducible inertially arbitrary patterns
Date: Monday, December 3, 2007
Time: 2.30 pm
Location: College West 307.20
Abstract: An n by n nonzero (resp. sign) pattern S is a matrix with entries in f ; 0g
(resp. fC; ; 0g). The inertia of a matrix A is the ordered triple .a1; a2; a3/ of nonnega
tive integers where a1 (resp. a2 and a3) is the number of eigenvalues of A with positive
(resp. negative and zero) real part. S is inertially arbitrary if each nonnegative integer
triple .a1; a2; a3/ with a1 C a2 C a3 D n is the inertia of a real matrix with nonzero
(resp. sign) pattern S. Some observations regarding which inertias nonzero (resp. sign)
patterns S and T may allow to guarantee that the direct sum S ° T is inertially arbitrary
are presented. It is shown that there exists noninertiallyarbitrary nonzero (resp. sign)
patterns S and T such that the direct sum S ° T is inertially arbitary.
AMS Subject Classifications: 15A18
Supervisors: S Fallat & S Kirkland
