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# A Question about eignvalues and eignvectors... watch

If A is invertible, then A is diagonalizable...I said it's false, because an invertible matrix does not necessarily have "n" distinct eignvalues and so may not be diagonalizable...is my answer correct?
2. Your answer's right, but the justification isn't. For example is diagonalisable (in fact, it's diagonal) but it doesn't have 2 distinct eigenvalues.

The best idea to "justify your answer" here would be to find an example of a matrix which is invertible but not diagonalisable.
3. Incidentally, I find it pretty unlikely you will be asked this question unless you've explicitly been shown examples of matrices that aren't diagonalizable in your course.
4. (Original post by DFranklin)
Incidentally, I find it pretty unlikely you will be asked this question unless you've explicitly been shown examples of matrices that aren't diagonalizable in your course.
I was asked this question after being told to read some theorems and read some examples...these are the theorems:

Theorem 1:

An nxn matrix A is a diagonalizable if and only if A has n linearly independet eigenvectors. In fact, A = PDP^(-1), with D a diagonal matrix, if and only if hte columns of P are n linearly independent eigenvectors of A. In this case, the diagonal entries of D are eignvalues of A that correspond, respectively, to the eigenvectors in P.

Theorem 2:

An nxn matrix with n distinct eigenvalues is diagonalizable.
5. And they didn't given you an example of a matrix where A doesn't have n lin.indep. eigenvectors? Strange.
6. (Original post by DFranklin)
And they didn't given you an example of a matrix where A doesn't have n lin.indep. eigenvectors? Strange.
Yes they did...anyways I get it now...thank you

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Updated: April 11, 2011
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