Real Semi-Inner Product Space is Complex Semi-Inner Product Space
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Theorem
Let $\struct{V, \innerprod \cdot \cdot}$ be a real semi-inner product space.
Then $\struct{V, \innerprod \cdot \cdot}$ is a complex semi-inner product Space.
Proof
This follows immediately from:
- Definition of Real Semi-Inner Product Space
- Definition of Complex Semi-Inner Product Space
$\blacksquare$