Let (V, \langle \cdot, \cdot \rangle) an Euclidean vector space
and v, u \in V with {\color{blue}\langle v,u \rangle = A}.
Determine the value of the scalar product \langle Cv, Bu \rangle.
\langle Cv, Bu \rangle
=
C*A*B
Using the bilinear property, we have \langle Cv, Bu \rangle =
C \cdot \langle v, Bu \rangle = C \cdot B \cdot {\color{blue}\langle v,u \rangle}.
Substituting {\color{blue}\langle v,u \rangle = A} yields
\langle Cv, Bu \rangle = C*A*B .