bigball1 写了: 2023年 2月 13日 21:11
扯尼玛蛋 你让丫给给哥做个 baynes network的题
Please use the similarity matrix method to calculate the 30th number of the fibonacci series? Please give the calculation steps.
We can use the properties of similarity matrices to quickly calculate the $n$th number in the Fibonacci sequence.
Let $A = \begin{bmatrix} 1 & 1 \ 1 & 0 \end{bmatrix}$. Then, $A^n = \begin{bmatrix} F_{n+1} & F_n \ F_n & F_{n-1} \end{bmatrix}$, where $F_n$ is the $n$th number in the Fibonacci sequence.
If we find the eigenvector $\mathbf{v}$ and corresponding eigenvalue $\lambda$ of matrix $A$, i.e. $A \mathbf{v} = \lambda \mathbf{v}$, then we can quickly calculate $A^n \mathbf{v} = \lambda^n \mathbf{v}$.
The steps are as follows:
Find the eigenvalue $\lambda$ and eigenvector $\mathbf{v}$ of matrix $A$.
Calculate $\lambda^n$ and $\mathbf{v}$.
From $A^n \mathbf{v} = \lambda^n \mathbf{v} = \begin{bmatrix} F_{n+1} \ F_n \end{bmatrix}$, we have $F_{30} = A^{30}_{2,1} = 832040$.
Therefore, the 30th number in the Fibonacci sequence is 832040.