An envelope-type region E(A) in the complex plane that contains the eigenvalues of a given n × n complex matrix A is introduced. E(A) is the intersection of an inﬁnite number of regions deﬁned by cubic curves. The notion and method of construction of E(A) extend those of the numerical range of A, which is known to be an intersection of an inﬁnite number of half-planes; as a consequence, E(A) is contained in the numerical range and represents an improvement in localizing the spectrum of A.
Dept. of Mathematics, Washington State University, US