三阶不可约零-非零模式中的几乎惯量任意模式

The Nearly-Inertially Arbitrary Irreducible Zero-Nonzero Patterns of Order 3

利用矩阵理论和组合论的方法对三阶不可约零-非零矩阵模式的惯量进行了研究,得到三阶不可约零-非零模式中所有几乎惯量任意的不可约零-非零模式,并将三阶不可约零-非零模式分为三类:惯量任意的不可约零-非零模式、几乎惯量任意的不可约零-非零模式、非惯量任意又非几乎惯量任意的不可约零-非零模式,并逐一验证.以几乎惯量任意的三阶不可约零-非零模式为基础,进一步验证了集合作为三阶不可约零-非零模式惯量临界集的必要条件,同时给出集合作为三阶不可约零-非零模式精细惯量临界集的一个必要条件.

By the method of matrix theory and combinatorial theory,the inertias of irreducible zero-nonzero patterns of order 3was focused on.The inertia almost arbitrary irreducible zero-nonzero patterns of the irreducible zero-nonzero patterns of order 3 were all identified.Then the irreducible zero-nonzero patterns of order 3were divided into three types and checked one by one,which included inertially arbitrary irreducible zero-nonzero patterns,nearly-inertially arbitrary irreducible zero-nonzero patterns,non-inertially arbitrary and non-nearly-inertially arbitrary irreducible zero-nonzero patterns.As a base,the necessary condition for a set as a critical set of inertia for irreducible zero-nonzero pattern of order 3obtains further investigated.Furthermore,a necessary condition that a set to be a critical set of refined inertia for irreducible zero-nonzero pattern of order 3is also presented.