A simplified Brauer's theorem on matrix eigenvalues
The spectrum inclusion region \(\widetilde\Omega\) of matrix eigenvalues is determined. It is simpler and tighter than those in Brauer's theorem and in \textit{X. Zhang} and \textit{D. Gu}'s work [Linear Algebra Appl. 196, 163-174 (1994; Zbl 0801.15016)]. All eigenvalues of the matrix are contained in \[ \widetilde\Omega= \bigcup_{a_{ij}\neq 0,i\neq j}\{z\in\mathbb{C}:|z-a_{ii}||z-a_{jj} |\leq r_ir_j\}. \] The number of ovals in Brauer's theorem is reduced in many cases. Eigenvalues and eigenvectors that are in the boundary of \(\widetilde\Omega\) are discussed.
scientific article; zbMATH DE number 1367956