一类非奇异F-矩阵的Oppenheim型不等式  

Oppenheim - like inequalities for a class of nonsingular F - matrices

作　　者：周景新[1] 杨忠鹏[2] 

机构地区：[1]北华大学数学系,吉林吉林132013 [2]莆田学院数学系,福建莆田351100

出　　处：《哈尔滨工业大学学报》2002年第6期853-857,共5页Journal of Harbin Institute of Technology

基　　金：福建省教育厅科学基金项目(JB01206).

摘　　要：研究了非奇异的F-矩阵类NFn上的Oppenheim型不等式,得到:如果A=(aij),B=(bij)εNFn的每个顺序主子阵Ak、Bk满足det Ak→Bk>0,β(Ak→Bk)≥bkkβ(Ak)+akkβ(Bk)-β(Ak)β(Bk)(其中β(Ak)=det Ak/det Ak-1),则A,B的Hadamard乘积的行列式det A→B≥a11b11(?)(bkkβ(Ak)+akkβ(Bk)-β(Ak)β(Bk))≥(?bii)det A+(?)detB-det Adet B+det A(?) (bnndet Bn-1-detb)+detB(?)(anndet An-1-detA).由此可加强正定Hermitian矩阵、M-矩阵上的Oppenheim型不等式.A matrix is called F - matrix, if each of its principal submatrix satisfies the Fischers inequality. The Oppenheim - like inequalities was investigated for the class NFn of nonsingula F - matrices, and the estimate of lower bound was given for del erminant over NFn . It is known that if k X k leading principal submatri-cesAk,Bk ,ofA = (atj) ,B = (bij)εNFn satisfy detAk - Bk > 0,β(Ak - Bk) ≥bkkβ(Ak) + akkβ(Bk) -β(Bk) ,then the del erminant of Hadamard product del A-B≥ a11b11(?) (bkkβ(Ak) + akkβ(Bk)-β(Ak)β(Bk))≥(?)det A + ( ? )det B -del Adet B + del A B where β(Ak) =Since the class matrices NF, contains Her-mitian positive definite matrices and M - matrices, our results strengthen the known results of the Oppenheim - like inequalitiesover these class matrices

关 键 词：非奇异F-矩阵 HADAMARD乘积 Fan乘积 OPPENHEIM型不等式 

分 类 号：O151.21[理学—数学]