2×2 matrix with one single eigenvalue, but two linearly independent eigenvectors?

Question

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!

score 5 · Accepted Answer · answered Mar 25 '15 at 18:49

5

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

answered Mar 25 '15 at 18:49

AlexR

24,905

1

(Found my inspiration: W is an answer) – AlexR Mar 25 '15 at 19:09
That's amazing, and now the torch has been passed on... – Zach466920 Mar 25 '15 at 19:24

score 0 · Answer 2 · answered Mar 25 '15 at 19:01

0

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.

answered Mar 25 '15 at 19:01

Doug Morgan

41

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

2×2 matrix with one single eigenvalue, but two linearly independent eigenvectors?

2 Answers2