4-number-problem/Ordered by size/Matrix/Exercise

We consider the mapping

$\Psi \colon \mathbb {R} _{\geq 0}^{4}\longrightarrow \mathbb {R} _{\geq 0}^{4},$

which assigns to a four-tuple ${}(a,b,c,d)$ the four-tuple

$(\vert {b-a}\vert ,\vert {c-b}\vert ,\vert {d-c}\vert ,\vert {a-d}\vert ).$

Describe this mapping with a matrix, under the condition

${}a\leq b\leq c\leq d\,.$

Create a solution