厄米特三对角复模式的惯量(英文)

Inertia Sets of Hermitian Tridiagonal Ray Patterns

讨论了元素为0或EIΘ的矩阵称为复模式.当EIΘ=1(EIΘ=-1)时,记EIΘ=+(EIΘ=-).若复模式A满足A=A*,称A为厄米特复模式.得出了复模式是符号模式的推广.设A,B∈MN(C)是给定的两个矩阵,如果存在非奇异矩阵S使得B=SAS*,则称B与A是相合的.利用相合的概念,给出了厄米特三对角复模式的惯量.

A matrix whose entries are either 0 or e^iθ, where θ∈R, is called a ray pattern. When e^iθ=1 （respectively, e^iθ=-1）, it denoted that e^iθ=＋ （respectively, e^iθ=-）. If a ray pattern A satisfies A=A^＊, such a pattern is called A Hermitian ray pattern. A ray pattern is a natural generalization of the concept of a sign pattern. Let A,B∈Mn（C） be two given matrixes. If there exists a nonsingular matrix S making B=SAS^＊, then B is said to be congruent to .4. In this paper, the authors has presented the inertia sets of n ×n Hermitian tridiagonal ray patterns using matrix congruence concept.