Toronto Math Forum
MAT2442018F => MAT244Lectures & Home Assignments => Topic started by: Shlok Somani on November 14, 2018, 10:26:25 PM

when we find the eigenvector from the corresponding eigenvalues shouldn't the vectors be (i, 1) and (i, 1)?

Seems to me that the vectors you proposed differ from the ones in textbook by a constant.

If $\xi$ is an eigenvector, corresponding to eigenvalue $k$, so is $\alpha \xi$ ($\alpha$, $\beta$ are scalars).
If $\xi^{(1)}$ and $\xi^{(2)}$ are eigenvectors, corresponding to the same eigenvalues $k$, so is $\alpha \xi^{(1)} +\beta \xi^{(2)}$

After you find the eigenvalue, you need to bring the eigenvalues (such as b) to the matrix ( P  bI ) to obtain the corresponding eigenvectors.