The skew energy of tournaments

Let S be the skew-adjacency matrix of a digraph. The skew energy of S, denoted by E(S), is the sum of the absolute values of the all eigenvalues of S. In this paper, for skew-adjacency matrices of tournaments of order n, we will give lower and upper bounds of the skew energy. We show that our lower bound is tight in the sense that it coincides with the minimum of E(S) of all skew-adjacency matrices of tournaments of order n. In addition, we will introduce the α-skew energy which is a generalization of the skew energy.