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I have an assignment where I need to create 2x2 matrices for each of the following Eigenvalue pairs.

i) eigenvalues are 2 and -3 ii) eigenvalues are 2+i and 2-i iii) eigenvalues are 1/2+2i and 1/2-2i 

I got the first one just by putting a 0 in one corner and 2 -3 along the diagonal, but I really have no clue how to get an complex number for an eigenvalue. Please someone help me understand!

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    yes they have to be real entries. I think this will help tho2011-12-08

1 Answers 1

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It's pretty easy to generate a $2\times 2$ matrix with real entries and conjugate eigenvalues. If you have

$\begin{pmatrix}a&c\\d&a\end{pmatrix}$

then the eigenvalues of this matrix are $a\pm\sqrt{cd}$.