An eigenvalue inequality and spectrum localization for complex matrices
Μαρία Αδάμ, Michael J. Tsatsomeros · Electronic Journal of Linear Algebra · 2006
Using the notions of the numerical range, Schur complement and unitary equivalence,an eigenvalue inequality is obtained for a general complex matrix, giving rise to a region in thecomplex plane that contains its spectrum. This region is determined by a curve, generalizing andimproving classical eigenvalue bounds obtained by the Hermitian and skew-Hermitian parts, as well as the numerical range of a matrix.