Write and Suppose that we take The possible values of X satisfying the given restrictions are where p and q are arbitrary. Then and
The eigenvalues of a 2x2 matrix are given by where is the trace of T, and is its determinant. If the eigenvalues are real, then the spectral radius (the larger of their absolute values) is given by
Applying that to the above matrices and , you see that and (noting that has real eigenvalues for all values of p and q)
Thus for all X satisfying the given constraints, but also. So (2) holds, but not (1).