Numerical range of matrices and Levinger's theorem (Q1893087)

This work is, in a sense, a continuation of the author's earlier work [ibid. 37, 81-96 (1981; Zbl 0452.15024)] on the numerical range of matrices. In particular, its connection to \textit{B. W. Levinger's} theorem [An inequality for nonnegative matrices. Notices Am. Math. Soc. 17, 260 (1970)] for the case of nonnegative matrices is extended for general complex matrices. Also, an elementary proof of Levinger's theorem is given.