Inverse closed ray-nonsingular cones of matrices

A description is given of those ray-patterns, which will be called inverse closed ray-nonsingular, of complex matrices that contain invertible matrices only and are closed under inversion. Here, two n × n matrices are said to belong to the same ray-pattern if in each position either the entries of both matrices are zeros, or both entries are nonzero and their quotient is positive. Possible Jordan forms of matrices in the inverse closed ray-nonsingular ray-patterns are characterized.