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?