Exercise 1.3.9

Answers

The cyclic difference matrix $C$ has a line of solutions (in 4 dimensions) to $Cx = 0$ :

\begin{gathered} [\begin{matrix} 1 & 0 & 0 & - 1 \\ - 1 & 1 & 0 & 0 \\ 0 & - 1 & 1 & 0 \\ 0 & 0 & - 1 & 1 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \\ x_{4} \end{matrix}] = [\begin{matrix} 0 \\ 0 \\ 0 \\ 0 \end{matrix}] when x = [\begin{matrix} c \\ c \\ c \end{matrix}] = any constant vector. \end{gathered}

mathchakra

2021-11-20 14:15