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

We consider the mapping

which assigns for a four-tuple the four-tuple

Describe this mapping with a matrix, under the condition

We consider the mapping

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

which assigns for 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

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