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@venik venik/latex
Last active Oct 17, 2017

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S_{N} = S_{N-2} + S_{N-1}
A = \left[\begin{array}{cc} 0 & 1\\ 1 & 1 \end{array}\right]
A \left[\begin{array}{cc} S_{N-2} \\S_{N-1} \end{array}\right] =
\left[\begin{array}{cc} 0 & 1\\ 1 & 1 \end{array}\right] \left[\begin{array}{cc} S_{N-2} \\S_{N-1} \end{array}\right] =
\left[\begin{array}{cc} S_{N-1} \\ S_{N} \end{array}\right]
\left[\begin{array}{cc} 0 & 1\\ 1 & 1 \end{array}\right] \left[\begin{array}{cc} 0 & 1\\ 1 & 1 \end{array}\right] \left[\begin{array}{cc} S_{0} \\S_{1} \end{array}\right] =
\left[\begin{array}{cc} 0 & 1\\ 1 & 1 \end{array}\right] \left[\begin{array}{cc} S_{1} \\S_{2} \end{array}\right] =
\left[\begin{array}{cc} 0 & 1\\ 1 & 1 \end{array}\right]^2 \left[\begin{array}{cc} S_{0} \\S_{1} \end{array}\right] =
\left[\begin{array}{cc} S_{2} \\S_{3} \end{array}\right]
A = S \Lambda S^{-1}
A^2 = A = S \Lambda S^{-1} S \Lambda S^{-1} = S \Lambda I \Lambda S^T = S \Lambda^2 S^{-1}
A^N = S \Lambda^N S^{-1}
A^2 = A = S \Lambda S^{-1} S \Lambda S^{T} = S \Lambda I \Lambda S^T = S \Lambda^2 S^T
http://www.sciweavers.org/free-online-latex-equation-editor
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