### Author Topic: Example 1 in section 7.6 of the textbook  (Read 1626 times)

#### Shlok Somani

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##### Example 1 in section 7.6 of the textbook
« 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)?

#### Tzu-Ching Yen

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##### Re: Example 1 in section 7.6 of the textbook
« Reply #1 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.

#### Victor Ivrii

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##### Re: Example 1 in section 7.6 of the textbook
« Reply #2 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 $\alpha \xi^{(1)} +\beta \xi^{(2)}$

#### Chutong(Peng) Judy

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##### Re: Example 1 in section 7.6 of the textbook
« Reply #3 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.