Math 210-01: Linear Algebra: Reading Homework 5.3

1. Orthonormal Bases: Gram-Schmidt : what types of bases are more convenient? why didn't we make this distinction before we got to chapter 5? what does the Gram-Schmidt process do?
   
   1. Orthogonality and Orthonormality : what do we mean by orthogonal and orthonormal sets?
      
      1. orthogonality and linear independence : how is orthogonality related to linear independence?
         
      2. orthogonality and basis : how is orthogonality related to bases for a vector space?
         
   2. Coordinates and Orthonormal Bases : what is the coordinate representation of a vector with respect to an orthonormal basis?
      
   3. Gram-Schmidt : what are the three steps of the Gram-Schmidt process?
      
      1. Gram-Schmidt : what is the mechanical procedure by which the second step of the Gram-Schmidt process is carried out?