Dot Product
Overview
The dot product is the standard
inner product
that is used in {% \mathbb{R}^n %}
{% \vec{x} = (x_1,x_2, ... ,x_n) %}
{% \vec{x} \cdot \vec{y} = \sum_i x_i y_i %}
Geometric Interpretation
{% \vec{x} \cdot \vec{y} = |\vec{x}| |\vec{y}| cos(\theta) %}
Projection
{% (\vec{x} \cdot \vec{y}) \vec{x} %}
where {% \vec{y} %} is a vector of unit length.
