Toronto Math Forum

MAT244--2018F => MAT244--Lectures & Home Assignments => Topic started by: Shlok Somani on November 14, 2018, 10:26:25 PM

Title: Example 1 in section 7.6 of the textbook
Post 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)?

Title: Re: Example 1 in section 7.6 of the textbook
Post by: Tzu-Ching Yen on November 14, 2018, 10:55:58 PM

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

Title: Re: Example 1 in section 7.6 of the textbook
Post by: Victor Ivrii on November 15, 2018, 12:00:41 AM

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 $\alpha \xi^{(1)} +\beta \xi^{(2)}$

Title: Re: Example 1 in section 7.6 of the textbook
Post by: Chutong(Peng) Judy on November 17, 2018, 02:05:55 AM

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