Eigenvalues and Eigenvectors

Part 3: No real eigenvalues

1. Enter the matrix B defined in the worksheet. Compute its characteristic polynomial, and use the result to explain why B has no real eigenvalues.



2. Use a built-in command to calculate the eigenvalues of B. Explain what your computer algebra system does in this case.



3. Construct a matrix Q whose columns are eigenvectors. What should Q^-1BQ be? Compute it to test your answer -- or perhaps to test your computer algebra system. If you have a built-in command for constructing a matrix whose columns should be eigenvectors, also try using this command to construct Q.

---

modules at math.duke.edu