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

Abstract

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.

Keywords

• 2-fold vector cross product
• hermitian inner product
• skew-symmetric matrix
• generalized inverse
• (vector cross product, vector cross product differential, vector cross product difference) equation
• primary 15a72
• secondary 15b57, 15a09