Question

what is inner product spaces?

Answer 1

An inner product space is a vector space in which an inner product is defined.

For example, the dot product is an inner product defined for \(\mathbb{R}^n\) for \(n\ge2\), with
\[a\cdot b=\sum_{i=1}^na_ib_i\]
for vectors \(a\) and \(b\) in \(\mathbb{R}^n\).