Given a split number $n=a+bj$, its inverse is $(a-bj)/(a^2-b^2)=n^*/nn^*$ A similar thing holds for complex and duel numbers. However, it fails for split numbers if $a^2=b^2$ and for dual numbers if $b=0$
What are the invertibility conditions for a general multivector in $Cl^{\infty,\infty,\infty}(\mathbb{R})$
Is it true that all vectors $(\sum_{i=0}^n a^i e_i)^2=\sum_{i=0}^n (a^i)^2$ is true where $e_i^2=1$?
I know that other questions like this have been asked and I could use matrices, but this is different in that it asks the actual algebraic conditions for invertibility.