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What is an an example of a $5\times 5$ matrix with exactly $2$ distinct eigenvalues? Also, what would be the eigenvalues in the example?

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Since you have a an answer here, please consider deleting your VERY recent duplicate: math.stackexchange.com/questions/351587/… –  amWhy Apr 4 '13 at 23:36

1 Answer 1

Trivial example:

$$\begin{pmatrix}1&0&0&0&0\\0&1&0&0&0\\0&0&1&0&0\\0&0&0&1&0\\0&0&0&0&2\end{pmatrix}$$

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What are the eigenvalues? –  jsjsjsd Apr 4 '13 at 23:34
    
This is a weird question...but anyway: look at the main diagonal... this is a diagonal matrix! –  DonAntonio Apr 4 '13 at 23:35
    
I understand, but what are the two distinct eigenvalues? –  jsjsjsd Apr 4 '13 at 23:36
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If you ask again then you don't understand, and I assumed anyone asking such a question should know that the eigenvalues of a diagonal matrix are the elements on its main diagonal... –  DonAntonio Apr 4 '13 at 23:38
    
does 1,1,2,2,2 have 2 distinct eigenvalue as well? –  jsjsjsd Apr 4 '13 at 23:45

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