Inner Product
Table of Contents
https://en.wikipedia.org/wiki/Inner_product_space
For Complex Numbers, inner product is defined as:
\begin{equation*} \langle x , y \rangle = \sum_i x_i \bar{y_i} \end{equation*}because, \(\langle x, x \rangle \geq 0\) requires \(\sum_i x_i x_i\) to be real. This hold for Real Numbers but not for complex numbers. Thus a conjugate is required.
1. Inner Product Space
An inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product.
