Real Inner Product Space is Complex Inner Product Space
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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:
- Definition of Real Inner Product Space
- Definition of Complex Inner Product Space
$\blacksquare$