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( \alpha + \alpha^{2} +\alpha^{4} )^{*} = \alpha^{*} + \alpha^{2} ^{*} +\alpha^{4} ^{*}
\displaystyle[br]\begin{equation*} \mathbf{I} + \mathbf{M} + \mathbf{M}^2 + \cdots + \mathbf{M}^{m-1} = \mathbf{I}\left(\mathrbf{I} - \mathbf{M}^m\right)(\mathbf{I}-\mathbf{M})^{-1} \end{equation*}
\displaystyle[br]\begin{equation*} \mathbf{I} + \mathbf{M} + \mathbf{M}^2 + \cdots + \mathbf{M}^{m-1} = \mathbf{I}\left(\mathrbf{I} - \mathbf{M}^m\right)(\mathbf{I}-\mathbf{M})^{-1} \end{equation*}
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