I read that geometric product $ab$ can be decomposed into 2 parts (symmetric and antisymmetric).
But I can't understand why symmetric part is a scalar product.
I mean following symmetric part:
$\frac{1}{2} (ab+ba) = \frac{1}{2}((a+b)^2-a^2-b^2)$
Why $ab+ba = (a+b)^2-a^2-b^2$ and $\frac{1}{2} (ab+ba) = a \cdot b $ ?
Thanks.