0x66cee410

A classical non-trivial example for a contravariant 2-tensor is a matrix. Since \(\mathbb{R}^{n\times n}=\mathbb{R}\otimes \mathbb{R}\) and the tensor product may defined via

\begin{equation*} (v\otimes w)^{ij}=v^iw^j. \end{equation*}

The so defined tensor product is bilinear.