In 2015, Armario conjectured that there exists a skew-symmetric EW matrix of order $4t+2$ if and only if there exists a tournament matrix $A$ with characteristic polynomial \[ \chi_A(x) = \left ( x^3 - (2t-1)x^2 - t(4t-1) \right ) \left ( x^2+x+t \right )^{2t-1}. \] In this talk, we prove Armario's conjecture . This is based on joint work with Gary Greaves.