Bilinear Basis

A bilinear basis is a Basis, which satisfies the conditions

$\begin{displaymath} (a{\bf x}+b{\bf y})\cdot {\bf z} = a({\bf x}\cdot{\bf z})+b({\bf y}\cdot{\bf z}) \end{displaymath}$

$\begin{displaymath} {\bf z}\cdot (a{\bf x}+b{\bf y}) = a({\bf z}\cdot{\bf x})+b({\bf z}\cdot{\bf y}). \end{displaymath}$

See also Basis