General Relativity: An Introduction for Physicists · Problem 4.1

Tensor calculus on manifolds — Hobson, Efstathiou & Lasenby

Physics · tensor-rank-2-linearity

Problem

\boldsymbol{t}

is a rank-2 tensor, show that

\boldsymbol{t}(\boldsymbol{u}+\boldsymbol{v}, \boldsymbol{w}+\boldsymbol{z}) = t_{ab}(u^a+v^a)(w^b+z^b).