Random Antagonistic Matrices
  The ensemble of antagonistic matrices is introduced and studied. In antagonistic matrices the entries $\mathcal A_{i,j}$ and $\mathcal A_{j,i}$ are real and have opposite signs, or are both zero, and the diagonal is zero. This generalization of antisymmetric matrices is suggested by the linearized dynamics of competitive species in ecology. 
Giovanni M. Cicuta and Luca Guido Molinari
math-ph cond-mat.stat-mech math.MP q-bio.PE