An invertibility criterion for multivectors in a real Clifford algebra

We derive an invertibility criterion for elements of a special type in the classical Clifford algebra $C_n$, namely for elements that are linear combinations of the basic elements $e_\alpha$ of the Clifford algebra $C_n$ with pairwise disjoint nonempty supports a $\alpha\subset\{1,2,\ldots,n\}$. The criteria is of a constructive character and consists in checking a finite number of conditions of linear type on the coefficients of such elements. For lower dimensions $n\le5$ we obtain an invertibility criterion for arbitrary elements of the Clifford algebra $C_n$ (also in terms of coefficients in expansion with respect to the standard basis).