= Tensor field
{title2=$\Gamma((T^*M)^{\otimes k}\otimes(TM)^{\otimes l})$}
{wiki}
A <tensor field> is a smooth <section of a vector bundle> formed from <tensor products> of the <tangent bundle> and <cotangent bundle>. With $k$ covector factors and $l$ vector factors it belongs to
$$
\Gamma\bigl((T^*M)^{\otimes k}\otimes(TM)^{\otimes l}\bigr).
$$
Its coefficients in any local frame vary smoothly. Different conventions list the two counts in different orders, so the factor order should be specified. <Tensor contractions> use the canonical evaluation of a covector on a vector and are independent of the frame.
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