What is the coefficient matrix of the Fibonacci sequence equation?


 

 

 

 

The Fibonacci sequence is a sequence of numbers in which each number is the sum of the two preceding ones, starting from 0 and 1: 0, 1, 1, 2, 3, 5, 8, 13, 21, ...  

The Fibonacci sequence can be represented by the linear homogeneous recurrence relation:  F(n) = F(n-1) + F(n-2)  Where F(n) represents the n-th number in the sequence. 

To find the coefficient matrix for this equation, we can write it in matrix form as:  [F(n), F(n-1)] = [F(n-1), F(n-2)] * [1, 1; 1, 0]  The matrix [1, 1; 1, 0] is the coefficient matrix for this equation. 

It represents the transformation that maps the n-1th and n-2nd numbers in the sequence to the nth number. 

This matrix is called the Fibonacci matrix and it plays a crucial role in various areas of mathematics and science, including number theory, graph theory, and the study of dynamical systems.

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