Real Inner Product Space is Complex Inner Product Space

Theorem
Let $\R$ be the field of real numbers.

Let $\GF$ be a subfield of $\R$.

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:






 * User:Leigh.Samphier/Refactor/Real Inner Product is Complex Inner Product

Also see

 * User:Leigh.Samphier/Refactor/Real Semi-Inner Product Space is Complex Semi-Inner Product Space