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Math 2890 - Sample Chapter 5 Problems

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Chapter 5

5.1      Eigenvectors and Eigenvalues
5.2      The Characteristic Equation
5.3      Diagonalization
5.5      Complex Eigenvalues
5.6      Discrete Dynamical Systems
5.7      Applications to Differential Equations
5.8      Iterative Estimates for Eigenvalues
  1. Find an eigenvector for a matrix given an eigenvalue.
  2. Find the eigenvalue for a matrix given an eigenvector.
  3. Find the eigenvalues of a matrix.
  4. Diagonalize a matrix.
  5. Create a matrix with prescribed eigenvalues and eigenvectors.
  6. Find the eigenvalues and eigenvectors of a matrix.
  7. Analyze the behavior of the discrete dynamical system $x_{k+1}=A x_k.$
  8. Analyze the behavior of the differential equation $y'=A y.$
  9. Solve a Discrete Dynamical System.
  10. Solve an Initial Value Problem.
  11. Use the Power Method to estimate the dominant eigenvalue and its eigenvector for a matrix.
  12. Use the Inverse Power Method to estimate the smallest eigenvalue and its eigenvector for a matrix.
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