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:

$\blacksquare$

Also see