Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 4 / 37D / b / i / Solution

The map takes one covector argument and returns two vector slots, so $S$ has two contravariant and one covariant index. Its tensor type isor type $(2,1)$, with components $S^{ab}{}_c$.

Solved by gpt-5.6-sol high.