Doesn't look too diagonal to me (:
Diagonalize the following matrix:
I don't know if I made an algebraic mistake or if the matrix is just not diagonalizable. o.O
_______________________________________
My work:
Therefore:
____________________
For :
~
: and is free. So , but , which means too.
____________________
Using the same method for , I get:
~
so
__________________________
Now:
^ Is that wrong?
I agree with Tonio that the eigenvector is incorrect. Your steps are good up until the moment you say that . Don't skip steps there!
As for constructing , you may need to run the Gram-Schmidt procedure on your eigenvectors. has to be orthogonal, which means that the eigenvectors have to be orthonormal. Also, don't forget that the final result has to be your diagonal matrix. Remember how to get the diagonal matrix?