矩阵的Hadamard积和Fan积的特征值的界

The bounds for eigenvalues of the Hadamard product and Fan product of matrices

讨论了矩阵的Hadamard积和Fan积的最小特征值的下界问题.令Mn为所有非奇异M-矩阵的集合,(1)若A,B∈Mn,B-1=(βij),则τ(A B-1)≥min1≤I≤n2aiiβii-τ(A)βii+τ(Aτ()B-)aii;(2)若A,B∈Mn,则τ(A*B)≥1m≤Ii≤nn[aiiτ(A)+bτ(A)-τ(A)τ(B)].同时又将这两结果与有关文献的结果进行比较.

Hadamard and Fan product of lower bound of minimal eigenvalue problem for matrix are discussed. The following two results are proved. Let Mn, be the set of all n x n non-singular M-matrices. Firstly, if A, B ∈Mn,B^-1=（βy）,then τ（A.B^-1）≥min 1≤i≤n[2aiiβii-τ（A）-aii/τ（B）];if A,B∈Mn,then τ（A＊B）≥min 1≤i≤n[aiiτ（B）＋buτ（A）-τ（A）τ（B）].The two results are compared with conclusions of related Literiture.