Math 210-01: Linear Algebra: Reading Homework 5.2

1. Inner Product Spaces : what extension does this section make?
   
   1. Inner Products : how do we denote an inner product? how is it related to a dot product?
      
      1. properties : when is a function an inner product?
         
      2. inner product spaces : what is an inner product space?
         
   2. Definitions : in an inner product space, what are the norm of a vector, the distance between two vectors, and the angle between two vectors? when are two vectors orthogonal?
      
   3. Inequalities and Theorems :
      
      1. Cauchy-Schwartz : what is the Cauchy-Schwartz inequality for an inner product space?
         
      2. Triangle : what is the triangle inequality for an inner product space?
         
      3. Pythagorean : what is the Pythagorean theorem for an inner product space?
         
   4. Orthogonal Projections : what is the orthogonal projection of a vector in an inner product space onto another vector v?