On the location of the spectrum of hypertournament matrices

AbstractInclusion regions for the spectrum of a hypertournament matrix A are obtained, based on a complex curve that relates the real and imaginary parts of the eigenvalues. These results generalize and in certain cases improve the work of S. Kirkland [Linear and Multilinear Algebra 30 (1991) 261]. The bounds obtained depend on the variance of the score vector; their tightness is investigated using the notion of numerical range