🎬A tensor contraction only depends on its symmetric part if the contracted indices are symmetric in

A tensor contraction only depends on its symmetric part if the contracted indices are symmetric in the vectors

The contraction $T_{a b} v^a v^b$ computes a scalar from a tensor and a vector, and only the symmetric part of the tensor contributes. Without knowing the explicit values of $T_{a b}$ and $v^a$, the result represents a quadratic form whose value depends on both the tensor and the vector components.

Symmetric and Antisymmetric Tensor Contractions | Proof and Derivationviadean on Notion