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Commit115cc22

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Fibonacci: restore matrix power form
Maybe a dotted line would show the matrix [[F2, F1],[F1,F0]] can be viewed as two column vectors.Using only the matrix power saves one matrix-vector multiply.
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‎src/algebra/fibonacci-numbers.md

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@@ -157,7 +157,19 @@ F_{n}
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\end{pmatrix}
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$$
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where $F_1 = 1, F_0 = 0$.
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where $F_1 = 1, F_0 = 0$.
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In fact, since
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$$
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\begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix}
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= \begin{pmatrix} F_2 & F_1 \\ F_1 & F_0 \end{pmatrix}
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$$
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we can use the matrix directly:
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$$
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\begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix}^n
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= \begin{pmatrix} F_{n+1} & F_n \\ F_n & F_{n-1} \end{pmatrix}
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$$
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Thus, in order to find $F_n$ in $O(\log n)$ time, we must raise the matrix to n. (See [Binary exponentiation](binary-exp.md))
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