geometric meaning of inner product
Inner Product. The inner- or dot- product is a central concept in geometry and analysis. Inner products over vector spaces of real numbers are scalar-valued functions i.e. functionals. They are bivariate functions, taking two vectors a and b as inputs, and returning a single scalar value. f(a, b) as their output. Inner products encode many aspects of our geometric intuition such as lengths, distances, and angles. Vector spaces equipped with inner-products are called inner product spaces. In functional analysis, these are also called pre-Hilbert spaces. Geometric Definition. Points or elements in inner-product spaces can be represented as arrows pointing from the origin to the chosen point.