Identity tensor (${\mathrm{id}}_{TM}={\delta }^{\mu }{}_{\nu }$)

The identity tensor is the canonical type-$(1,1)$ tensor that maps each tangent vector to itself. It pairs a covector $\eta$ and vector $V$ as $\eta (V)$, and its components are the Kronecker delta ${\delta }^{\mu }{}_{\nu }$ in every coordinate system.