An introduction to inner product space (Part 1)

We introduce the definition of inner product space here (it's a vector space equipped with an operation called inner product).

The motivation is based on the dot product on the xy-plane.

We do a few exercises on the computations related to the use of inner product (like finding norm of a vector, finding distance between 2 vectors,, and some basic inner product computations).

Except the usual Euclidean space R^n and the common inner products associated with it, we also look at the standard inner product defined on the vector space of 2x2 matrices.