Math 210-01: Linear Algebra: Reading Homework 5.4

1. Mathematical Models and Least Squares Analysis : what is this section concerned with?
   
   1. Least Squares Regression Line : what is a least squares regression line? what does this have to do with the phrase ``best possible''?
      
      1. least squares problem : what do we mean by the ``least squares problem''?
         
   2. Orthogonal Subspaces : when are two subspaces orthogonal?
      
   3. Orthogonal Complement : what is the orthogonal complement of a subspace? how do we find the orthogonal complement of a subspace?
      
   4. Direct Sum : what is the direct sum of two subspaces?
      
   5. Orthogonal Subspaces : what properties do orthogonal subspaces have?
      
   6. Projection onto a Subspace : what do we mean when we project a vector onto a subspace? How is this related to the orthogonal complement of the subspace and to direct sums? Graphically, what do we mean by the projection of a vector (e.g., in R², onto another vector)?
      
      1. Orthogonal Projection and Distance : why is theorem 5.15 titled this?
         
   7. Fundamental Subspaces : what are the fundamental subspaces of a matrix? how are they related?
      
   8. Least Squares : what equation does the solution to the least squares problem solve? what properties of projections and fundamental subspaces are used in the derivation of this equation?