Let D be a digraph of order n with adjacency matrix A(D). For α ∈ [0, 1), the A α matrix of D is defined asIn this paper, we find the singular values of some basic digraphs and characterize the digraphs D with Rank (A α (D)) = 1. As an application of these results, we obtain a lower bound for the trace norm of A α matrix of digraphs and determine the extremal digraphs. In particular, we determine the oriented trees for which the trace norm of A α matrix attains minimum. We obtain a lower bound for the α spectral norm σ 1α (D) of digraphs and characterize the extremal digraphs. As an application of this result, we obtain an upper bound for the α trace norm of digraphs and characterize the extremal digraphs.