& 0\\
    (1,\mathbf{E}^{-}) & 0 & 0 & \cdots& 0 & 0 & \mV^{-} & \cdots& 0\\
    \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \ddots & \vdots \\
    (n-1,\mathbf{E}^{-}) & 0 & 0 & \cdots & 0 & 0 & 0 & \cdots & 0\\
    (n,\mathbf{E}^{-}) & 0 & 0 & \cdots& 0 & 0 & 0 & \cdots & \mV^{-}
  },\end{aligned}$$ $$\begin{aligned}
\label{eq:blockPi+}
  {\widetilde}{\Lambda}_{c}^{+}=
  \kbordermatrix{
    & (0,\mathbf{E}^{+}) & (1,\mathbf{E}^{+}) & \cdots & (n-1,\mathbf{E}^{+}) & (n,\mathbf{E}^{+}) \\
    (0,\mathbf{E}^{-}) &{\widetilde}{\Lambda}_{c,00}^{+} & {\widetilde}{\Lambda}_{c,01}^{+} & \cdots & {\widetilde}{\Lambda}_{c,0,n-1}^{+} & {\widetilde}{\Lambda}_{c,0n}^{+} \\
    (1,\mathbf{E}^{-}) & 0 & {\widetilde}{\Lambda}_{c,11}^{+} & \cdots & {\widetilde}{\Lambda}_{c,1,n-1}^{+} & {\widetilde}{\Lambda}_{c,1n}^{+} \\
    \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\
    (n-1,\mathbf{E}^{-}) & 0 & 0 & \cdots & {\widetilde}{\Lambda}_{c,n-1,n-1}^{+} & {\widetilde}{\Lambda}_{c,n-1,n}^{+} \\
    (n,\mathbf{E}^{-}) & 0 & 0 & \cdots & 0 & {\widetilde}{\Lambda}_{c,nn}^{+}
  }\end{aligned}$$ $$\begin{aligned}
\label{eq:blockPi-}
  {\widetilde}{\Lambda}_{c}^{-}=
  \kbordermatrix{
    & (0,\mathbf{E}^{-}) & (1,\mathbf{E}^{-}) & \cdots & (n-1,\mathbf{E}^{-}) & (n,\mathbf{E}^{-}) \\
    (0,\mathbf{E}^{+}) & {\widetilde}{\Lambda}_{c,00}^{-} & {\widetilde}{\Lambda}_{c,01}^{-} & \cdots & {\widetilde}{\Lambda}_{c,0,n-1}^{-} & {\widetilde}{\Lambda}_{c,0n}^{-} \\
    (1,\mathbf{E}^{+}) & 0 & {\widetilde}{\Lambda}_{c,11}^{-} & \cdots & {\widetilde}{\Lambda}_{c,1,n-1}^{-} & {\widetilde}{\Lambda}_{c,1n}^{-} \\
    \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\
    (n-1,\mathbf{E}^{+}) & 0 &0 & \cdots 