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# Definition

The Euclidean Inner Product is the Inner Product $\langle \cdot, \cdot \rangle: \mathbb{C}^{n} \to \mathbb{C}$ defined as

$$\langle \mathbf{x}, \mathbf{y} \rangle = \sum\limits_{i=1}^{n} x_{i}\bar{y_{i}}$$ for $\mathbf{x}, \mathbf{y} \in \mathbb{C}^{n}$.

# Euclidean Inner Product is an Inner Product

Proof: TODO - this is straightforward