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Can we have a 2×2 matrix with one single eigenvalue, but two linearly independent eigenvectors? Is this possible? If so, how?

Thanks for the help!

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$$\huge I_{2\times 2}{}{}{}{}{}{}$$

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    $\begingroup$ (Found my inspiration: W is an answer) $\endgroup$ – AlexR Mar 25 '15 at 19:09
  • $\begingroup$ That's amazing, and now the torch has been passed on... $\endgroup$ – Zach466920 Mar 25 '15 at 19:24
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If you remember eigendecomposition, you can write a matrix as RUR^-1, where R is the matrix of eigen-vectors, and U is a diagonal matrix containing the eigenvalues. Thus you can plug the linearly independent eigenvectors you want into R, as well as the single eigenvalue you want into U.

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  • $\begingroup$ You can write a diagonalizable matrix in this fashion (but of course this is what the OP wants). $\endgroup$ – Ian Mar 25 '15 at 19:03

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