The Perron eigenspace of nonnegative almost skew-symmetric matrices and Levinger's transformation (Q1863521)

An almost skew-symmetric matrix is a matrix \(A\) such that \(A+A^t\) has rank 1. For an almost-skew symmetric nonnegative matrix the authors obtain estimates on the eigenvalues of Levinger's transformation \[ L(A,\alpha)=(1-\alpha)A+\alpha A^t, \alpha \in [0,1/2] \] [cf. \textit{B. W. Levinger}, An inequality for nonnegative matrices. Notices Am. Math. Soc. 17, 260 (1970)].