Some thing is going wrong!
The eigenvalues are the sol of the following equation
that is
so this equation has a real valued solutions if and only if
which equivalently means
I got this problem:
Find the values of "z" for which this Matrix has no real eigenvalues.
The Matrix is the following:
[ 1 -1]
[ 1 z]
I tried to solve this problem as follows:
1) I calculated the eigenvalues for the Matrix keeping "z" as a constant
2) I got:
-1/z^{1/2} and 1/z^{1/2}
So if I substitute z with >0 I have real eigenvalues.
For z <0 I don't have real eigenvalues.
But what happens with the 0? If I substitute 0 for z the result is not defined, but if I substitute 0 for z in the matrix I get two real eigenvalues (0,0).
Therefore I say that the Matrix has no real eigenvalues for z<0
Is this true?