I tried landscape and rotating packages to rotate the equation. In both cases I received error messages!
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\begin{align*}&\left[ {\begin{array}{ccccccccccc}1 & -P(N_k^a|L_k^c) & 0 & 0 & 0 &0&\dots&0&0&0&0\\-P(N_{k+1}^d|L_{k+1}) & 1 & 0& -P(N_{k+1}^a|L_{k+1})& 0 &0&\dots&0&0&0&0\\-P(N_{k+1}^d|L_{k+1}^c) & 0 & 1 & -P(N_{k+1}^a|L_{k+1}^c)& 0 &0&\dots&0&0&0&0\\0 & 0 & -P(N_{k+2}^d|L_{k+2})& 1&0&-P(N_{k+2}^a|L_{k+2})&\dots&0&0&0&0\\0 & 0 & -P(N_{k+2}^d|L_{k+2}^c)& 0&1&-P(N_{k+2}^a|L_{k+2}^c)&\dots&0&0&0&0\\\vdots & \vdots & \vdots & \vdots & \vdots & \vdots&\ddots&\vdots&\vdots&\vdots&\vdots\\0 & 0 & 0&0&0&0&\dots& -P(N_{c-1}^d|L_{c-1})& 1 &0& -P(N_{c-1}^a|L_{c-1})\\0 & 0 & 0&0&0&0&\dots& -P(N_{c-1}^d|L_{c-1}^c)&0 & 1 & -P(N_{c-1}^a|L_{c-1}^c)\\0 & 0 & 0&0&0 &0&\dots&0 &0 & -P(N_c^d|L_c) & 1\end{array} } \right].\left[ {\begin{array}{c}E(\widetilde{A}_{kk}^{cn}|L_k^c)\\E(\widetilde{A}_{k k+1}^{cn}|L_{k+1})\\E(\widetilde{A}_{k k+1}^{cn}|L_{k+1}^c)\\E(\widetilde{A}_{k k+2}^{cn}|L_{k+2})\\E(\widetilde{A}_{k k+2}^{cn}|L_{k+2}^c)\\\vdots \\E(\widetilde{A}_{k c-1}^{cn}|L_{c-1})\\E(\widetilde{A}_{k c-1}^{cn}|L_{c-1}^c)\\E(\widetilde{A}_{kc}^{cn}|L_{c})\\\end{array} } \right]\\=&\left[ {\begin{array}{c}E(R_k|L_k^c) + P(N_k^s|L_k^c) E\left(\widetilde{B}_{kk}^{c+n}|L_k^c\right) \\E(R_{k+1}|L_{k+1}) + P(N_{k+1}^s|L_{k+1}) E\left(\widetilde{B}_{kk+1}^{c+n}|L_{k+1}^c \right)\\E(R_{k+1}|L_{k+1}^c) +P(N_{k+1}^s|L_{k+1}^c) E\left(\widetilde{B}_{kk+1}^{c+n}|L_{k+1}^c \right)\\E(R_{k+2}|L_{k+2}) + P(N_{k+2}^s|L_{k+2}) E\left(\widetilde{B}_{kk+2}^{c+n}|L_{k+2}^c \right)\\E(R_{k+2}|L_{k+2}^c) +P(N_{k+2}^s|L_{k+2}^c) E\left(\widetilde{B}_{kk+2}^{c+n}|L_{k+2}^c \right)\\\vdots \\E(R_{k+2}|L_{c-1}) + P(N_{c-1}^s|L_{c-1}) E\left(\widetilde{B}_{kc-1}^{c+n}|L_{c-1}^c \right)\\E(R_{k+2}|L_{c-1}^c) +P(N_{c-1}^s|L_{c-1}^c) E\left(\widetilde{B}_{kc-1}^{c+n}|L_{c-1}^c \right)\\E(\widetilde{A}_{kc}^{cn}|L_{c})\\\end{array} } \right]\end{align*}