高等学校计算数学学报(英文版)
高等學校計算數學學報(英文版)
고등학교계산수학학보(영문판)
MUMERICAL MATHEMATICS A JOURNAL OF CHINESE UNIVERSITIES ENGLISH SERIES
2001年
2期
226-240
,共15页
Frank J.Hall Li%李忠尚
Frank J.Hall Li%李忠尚
Frank J.Hall Li%리충상
inertia%sign pattern matrix%inertia set%unique inertia%Toeplitz matrix
A sign pattern matrix is a matrixwhose entries are from the set {+ ,- ,0}. The symmetric sign pattern matrices that require unique inertia have recently been characterized. The purpose of this paper is to more generally investigate the inertia sets of symmetric sign pattern matrices. In particular, nonnegative fri-diagonal sign patterns and the square sign pattern with all + entries are examined. An algorithm is given for generating nonnegative real symmetric Toeplitz matrices with zero diagonal of orders n≥3 which have exactly two negative eigenvalues. The inertia set of the square pattern with all + off-diagonal entries and zero diagonal entries is then analyzed. The types of inertias which can be in the inertia set of any sign pattern are also obtained in the paper. Specifically, certain compatibility and consecutiveness properties are established.
