矩阵特征值Ky Fan定理的另一个推广

Another Improvement on Ky Fan’s Theorem of Matrix Eigenvalues

任给 A∈ Mn( n≥ 2 ) ,且 A具有如下循环式分块形式A =A1 1 A1 2A2 2 A2 3 Ar- 1 ,r- 1 Ar- 1 ,rAr1 Arr,其中 Aii( i=1 ,… ,r)是 ni× ni阶方阵 ,ni满足 ∑ri=1 ni=n.通过 Perron- Frobenius定理 。

Let A∈M n, and A has the block form A=A 11 A 12 A 22 A 23  A r-1,r-1 A r-1,r A r1 A rr , where A ii (1≤i≤r) is n i×n i matrix and n i satisfies ∑r i=1 n i=n.In terms of Perron Frobenius theorem, we give a method to estimate the spectral radius of .