# Matrix not diagonalizable over C

• Mar 21st 2010, 02:59 PM
andrewdb
Matrix not diagonalizable over C
Hi my question is

Find all the values of k for which the matrix

0, 1, 0
0, 0, 1
0, -k-2, k+3

is not diagonalizable over C. i understand how to diagonlize matrices but i do
not understand what values of k make the above statement true.
• Mar 21st 2010, 06:44 PM
Moo
Hello,

I think you have no other choice than finding the characteristic polynomial and the eigenvalues.
Then find k such that at least one of the eigenspaces has a dimension < to the order of multiplicity of the eigenvalue...
• Mar 21st 2010, 09:17 PM
andrewdb
Quote:

Originally Posted by Moo
Hello,

I think you have no other choice than finding the characteristic polynomial and the eigenvalues.
Then find k such that at least one of the eigenspaces has a dimension < to the order of multiplicity of the eigenvalue...

Does that mean that the eigenvector corresponding to that eigenvalue has more parameters than does the multiplicity of the eigenvalue?