General Relativity: An Introduction for Physicists · Problem 4.2

Tensor calculus on manifolds — Hobson, Efstathiou & Lasenby

Physics · symmetric-antisymmetric-tensor-contraction

Problem

s_{ab} = s_{ba}

and

t_{ab} = -t_{ba}

are the component of a symmetric and an antisymmetric tensor respectively, show that

s_{ab}t^{ab} = 0