I have this difference equation:
$c_0 x_n+c_1x_{n+1}+\cdots+c_m x_{n+m} = \sum\limits_{i=0}^m c_i x_{n+i} = 0 $
And I have problem with understanding the dimension argument.
Dimension argument
Given $x_1,\ldots,x_m \Rightarrow x_{m+1} = -\dfrac{1}{c_m}\displaystyle\sum\limits_{i=0}^{m-1} c_i x_{n+i}$
Which means selection of $x_1,\ldots,x_m$ corresponds to picking a point in the m-dimensional space $\mathbb{R}^m$, so the solution space has dimension $m$.
And I don't understand the last part "Which means selection of ..". Someone who can explain it in details?