Skew-symmetric matrices related to the vector cross product in ℂ⁷

Skew-symmetric matrices of order 7 defined through the 2-fold vector cross product in ℂ⁷, and other related matrices, are presented. More concretely, matrix properties, namely invertibility, nullspace, powers and index, are studied. As a consequence, results on vector cross product equations, vector cross product differential equations and vector cross product difference equations in ℂ⁷ are established.