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This section is about the definition of the dot product over , which extends the definition of the dot product over .
Some motivation is discussed at: math.stackexchange.com/questions/2459814/what-is-the-dot-product-of-complex-vectors/4300169#4300169
The complex dot product is defined as:
E.g. in :
We can see therefore that this is a form, and a positive definite because:
Just like the usual dot product, this will be a positive definite symmetric bilinear form by definition.

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