Identity tensor
= Identity tensor
{title2=$\operatorname{id}_{TM}=\delta^\mu{}_{\nu}$}
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.