Recurrence Relationshard
0:00.0
The coupled recurrence system
$$x_n = 2x_{n-1} + y_{n-1}$
y_n = x_{n-1} + 2y_{n-1}$$
can be written as \begin{pmatrix} x_n \ y_n \end{pmatrix} = M \begin{pmatrix} x_{n-1} \ y_{n-1} \end{pmatrix}M = \begin{pmatrix} 2 & 1 \ 1 & 2 \end{pmatrix}$.
What are the eigenvalues (characteristic roots) of ?
The coupled recurrence system $$x_n = 2x_{n-1} + y_{n-1}$
y_n = x_{n-1} + 2y_{n-1}$$ can be written as \begin{pmatrix} x_n \ y_n \end{pmatrix} = M \begin{pmatrix} x_{n-1} \ y_{n-1} \end{pmatrix}M = \begin{pmatrix} 2 & 1 \ 1 & 2 \end{pmatrix}$.
What are the eigenvalues (characteristic roots) of ?