  This paper extends the "single crossing point" property of the scalar MMSE
function, derived by Guo, Shamai and Verd\'u (first presented in ISIT 2008), to
the parallel degraded MIMO scenario. It is shown that the matrix Q(t), which is
the difference between the MMSE assuming a Gaussian input and the MMSE assuming
an arbitrary input, has, at most, a single crossing point for each of its
eigenvalues. Together with the I-MMSE relationship, a fundamental connection
between Information Theory and Estimation Theory, this new property is employed
to derive results in Information Theory. As a simple application of this
property we provide an alternative converse proof for the broadcast channel
(BC) capacity region under covariance constraint in this specific setting.
