不可约M-矩阵的最小特征值的估计

The Estimation of the Smallest Eigenvalue of the lrreducible M-matrix

讨论了不可约M-矩阵A的最小特征值l(A)的估计问题。得到了,若A,B∈Rn×n是不可约M-矩阵。记B-1=[bij],A-1=[aij],则l(A oB-1)<2 m ax1 i nakkbkk,且存在正对角矩阵D1=d iag(d1,d2,∧,dn),与D2=d iag(d1,d2,∧,dn),使得m in1 i ndim in1 i ndi l(A)m ax1 i ndi1 m i a nxdi.

The smal1lest eigenvalue l（A） of irreducible M-matrix A= （αij）is discussed in this paper. It is shown that l （AoB^-1 ）〈2 maxαkk^bkk 1≤i≤n if A, B ∈ R^n×n are irreducible M-matrix where B^-1 = [^-bij], and that there exists positive diagonal matrix D1=ding（^-d1,d2,∧,dn）and D2=ding（^-d1,^-d,∧,^-dn）such that mindi 1≤i≤n min 1≤i≤n ^-di,≤l（A）≤maxdi 1≤i≤n max^-di 1≤i≤n.