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How do I determine if this matrix is diagonalisable? Even with the hint im not sure, thanks..

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- May 14th 2011, 04:21 PMqwerty1234Diagonalisable matrices
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How do I determine if this matrix is diagonalisable? Even with the hint im not sure, thanks.. - May 15th 2011, 02:01 AMOpalg
If x is in the range of M then x is an eigenvector (with eigenvalue 1). If x is in the kernel of M then x is an eigenvector (with eigenvalue 0). Now use the "rank plus nullity = n" theorem to conclude that the matrix has lots of eigenvectors.

- May 15th 2011, 02:58 AMtonio
- May 15th 2011, 04:16 AMDeveno
...and the problem explicitly gives you the minimal polynomial of M....