Math 210-01: Linear Algebra: Reading Homework 5.5

1. Applications of Inner-Product Spaces :
   
   1. Cross-Products : what is the cross-product of two vectors in R³?
      
      1. properties of cross-products : what are the geometric characteristics of cross-products?
         
   2. Least Squares in Calculus : what is the least squares approximation to a function with respect to a subspace of continuous functions? how does this depend on an interval?
      
      1. finding least-squares approximations : how can we find the linear least-squares approximation to a function on a given interval?
         
      2. finding least squares approximations : how can we use inner-products to find least-squares approximations to a function?
         
      3. Fourier approximations : how is a Fourier approximation related to the least-squares problem?