  Let $\lambda\in \mathbb{R},$ $\mu\in \mathbb{R}$ and $B$ be a linear bounded
operator from a Hilbert space $\mathcal{K}$ into another Hilbert space
$\mathcal{H}.$ In this paper, we consider the formulas of the absolute value
$|Q_{\lambda,\mu}|,$ where $Q_{\lambda,\mu}$ with respect to the decomposition
$\mathcal{H}\oplus\mathcal{K}$ have the operator matrix
  form $Q_{\lambda,\mu}:=\left(\begin{array}{cc}\lambda I&B\\B^*&\mu
I\end{array}\right).$ Then the positive part and the support projection of
$Q_{\lambda,0}$ are obtained. Also, we characterize the symmetry $J$ such that
a projection $E$ is the $J$-projection. In particular, the minimal element of
the set of all symmetries $J$ with the property $JE\geqslant0$ is described.
