E—matrices and Several Necessary and Sufficient Conditions

AER-x.,Aiscalledanonnegative(nonPositive)matrixifau>O(a,jO(aiirtO),markedA>O(AO(i#j),auO,wecallp(A)=max{IA,l,lA,l'.-.,lAnl},(whereA,,A2,..',A"areeigenva1ueofA)asspectralradiusofA.LemmalIfAe7'.,thenareanonnegativesquarematrxBandapositivenumberksuchthatA=B-kI(whereIistheidentitymatrixofordern).ProofLetbti=…     

A Kind of Square Matrices and Its Qualities

ＡＫｉｎｄｏｆＳｑｕａｒｅＭａｔｒｉｃｅｓａｎｄＩｔｓＱｕａｌｉｔｉｅｓ￥ＷｅｉＺｏｎｇｌｉ（ＬｕｏｙａｎｇＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ）Ａｂｓｔｒａｃｔ：ＴｈｉｓｐｅｐｅｒｄｉｓｃｕｓｓｅｓａｋｉｎｄｏｆＳｑｕａｒｅｍａｔｒｉｃｅｓｗｈｉｃｓｉｓ...     

有关E'-矩阵的若干注记

The class of E'-matrices introduced in [4] is a subclass of Q0-matrices whose proper principal submatrices are Q-matrices. In this paper, we investigate the relation of the class E' to other known matrix classes and obtain a series of necessary and sufficient conditions for E'-matrices.