A SIMPLIFIED BRAUER'S THEOREM ON MATRIX ELGENVALUES

摘要

Let A=(α_ij)∈C~n×n and r_i=∑+j≠i|α_ij|. Suppose that for each row of A there is at least one nonzero off-diagonal entry. It is proved that all eigenvlaues of A are contained in Ω=∪α_ij≠0,i≠ j{z ∈C:|z-α_ii||z-α_ij|≤r_ir_j}. The result reduces the number of oval sin original Brauer's theorem in many cases. Eigenvalues (and associated eigenvectors) that local in the boundary of Ω re discussed.