Real Inner Product is Complex Inner Product
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Theorem
Let $V$ be a vector space over a real subfield $\GF$.
Let $\innerprod \cdot \cdot: V \times V \to \GF$ be a real inner product.
Then $\innerprod \cdot \cdot$ is a complex inner product
Proof
This follows immediately from:
- Definition of Real Inner Product
- Definition of Complex Inner Product
$\blacksquare$