Vector Cross Product Differential and Difference Equations in R^3 and in R^7

Through a matrix approach of the $2$-fold vector cross product in $\mathbb{R}^3$ and in $\mathbb{R}^7$, some vector cross product differential and difference equations are studied. Either the classical theory or convenient Drazin inverses, of elements belonging to the class of index $1$ matrices, are applied.