Canonical tensors over a nondegenerate quadratic space

Let be a nondegenerate finite-dimensional quadratic space over . Consider a basis , and let be the corresponding dual basis. Then the element

is independent of the choice of , #m/thm/geoalg and so is its symmetrization

Alternate representation

Let be the linear isomorphism induced by and be the canonical isomorphism. Then

#state/tidy | #lang/en | #SemBr