对一类极小惯量任意符号模式矩阵的刻画

Characlerization of a New Class of Minimally Inertially Arbitrary Sign Patterns

若每个首项系数为1的n阶实系数多项式,其中xn-2的系数为正的多项式是Q(ψ)中一些矩阵的特征多项式,则称ψ是惯量任意的。如果一个惯量任意符号模式的任意非零元被零取代后得到的符号模式不是惯量任意的,那么这个惯量任意符号模式称为极小惯量任意符号模式。在前人已证明一族新的符号模式ψ2k+1(k≥2)是惯量任意的基础上,利用有固定惯量的矩阵的特征多项式的系数的一些性质对ψ13的极小性进行刻画。

If every monic real polynomial of degree n having a position coefficient of xn-2 is the characteristic polynomial of some matrix in Q（ψ）,then ψ is a inertially arbitrary pattern.A sign pattern ψ is minimally inertially arbitrary if it is inertially arbitrary but is not inertially arbitrary if any nonzero entry（or entries） of ψ is replaced by zero.Jac Kim and so on have proved a new family of sign patterns ψ2k＋1（k≥2） is inertially arbitrary.In this paper,based on the known properties of the coefficient of the characteristic polynomial of an arbitrary matrix,ψ13 is minimally Inertially arbitrary.