ABSTRACT
This chapter presents one way of forming the product of vectors, called the inner product that associates a scalar with each pair of vectors. It discusses complex numbers come more to the forefront. In a real inner product space, the projection P is orthogonal if the matrix representation of P is symmetric with respect to some basis. One of the most widely used and versatile methods in statistics is linear regression. A linear regression model may be used to predict Y for given values of the explanatory variables, or to describe the relationship of the explanatory variables to Y. Analysis may show which variables are useful in the model and which ones can be dropped without much loss of information. While the Euclidean inner product is the most often used inner product, there are applications where other inner products are useful.
