Chapter 3 Analytic Geometry
In Chapter 2, we explored vectors, vector spaces, and linear mappings at an abstract level. This chapter introduces geometric interpretation and intuition to these ideas, focusing on:
- Lengths and distances between vectors
- Angles between vectors
- Inner products and their induced geometry
- Orthogonal projections (important for PCA and regression)
The inner product introduces geometry into vector spaces by defining similarity, length, and distance.
