Eigenvalues and Eigenvectors

Part 2: The matrix P

We continue with the matrices A and P defined in Part 1.

1. Check that each column of P really is an eigenvector: Multiply each column by A, and verify that the result is the same as multiplying the column by the corresponding eigenvalue. How do you tell which eigenvalue corresponds to each column?



2. Interchange two columns of P, and calculate P^-1AP again. Explain the result.



3. Multiply each column of P by a different, nonzero scalar. Calculate P^-1AP again. Explain the result.

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