Math 224-01: Differential Equations: Reading Homework 7.4

1. Eigenvalues and Eigenvectors of Matrices :
   
   1. Eigenvalue Problems : what matrix equation are we solving to find eigenvalues and eigenvectors?
      
      1. Point : what is an eigenvalue? an eigenvector?
         
      2. Point : what is an eigenspace? how is it related to an eigenvector?
         
   2. Solving Eigenvalue Problems : how do we solve an eigenvalue problem? (how do we find the eigenvalues? the eigenvectors?)
      
      1. Point : why are we interested in the Eigenspace property? what does it tell us?
         
      2. Point : what is an eigenbasis?
         
      3. Point : what is a characteristic polynomial? what is the multiplicity of an eigenvalue? (how is this related to the polynomial?)
         
   3. Deficient Eigenspaces : what is a deficient eigenspace? how is it related to an eigenvalue?
      
      1. Point : what's a generalized eigenvector?
         
      2. Point : if we put regular and generalized eigenvectors together, are the vectors linearly independent? how many are there, total?