biVector forum

Solving system of Clifford equations

I’m interested in solving the following system of equations in \mathbb{Cl}(2,0):

\boldsymbol{Z}_{11}\boldsymbol{x}_1+\boldsymbol{Z}_{12}\boldsymbol{x}_2+\ldots+\boldsymbol{Z}_{1n}\boldsymbol{x}_n=\boldsymbol{a}_1
\boldsymbol{Z}_{21}\boldsymbol{x}_1+\boldsymbol{Z}_{22}\boldsymbol{x}_2+\ldots+\boldsymbol{Z}_{2n}\boldsymbol{x}_n=\boldsymbol{a}_2
.
.
.
\boldsymbol{Z}_{m1}\boldsymbol{x}_1+\boldsymbol{Z}_{m2}\boldsymbol{x}_2+\ldots+\boldsymbol{Z}_{mn}\boldsymbol{x}_n=\boldsymbol{a}_m

where \boldsymbol{Z}_{ij} are bivectors and \boldsymbol{a}_i are vectors. The unknowns are \boldsymbol{x}_i which are also vectors.

M. E. Horn used exterior algebra to solve a similar system where all the elements are scalars here (page 12).