Real Inner Product Space is Complex Inner Product Space

Theorem
Let $\struct{V, \innerprod \cdot \cdot}$ be a real inner product space.

Then $\struct{V, \innerprod \cdot \cdot}$ is a complex inner product Space.

Proof
This follows immediately from:






 * Real Inner Product is Complex Inner Product

Also see

 * Real Semi-Inner Product Space is Complex Semi-Inner Product Space