= Contravariant vector
{title2=$T'^a=(\partial x'^a/\partial x^b)T^b$}
A <contravariant vector> has coordinate components obeying the displayed transformation law. A <tangent vector> to a parametrized curve provides the basic example: the <chain rule> transforms $dx^a/ds$ in precisely this way. Pairing it with a <covector> produces a coordinate-independent <scalar>. Conversely, if an array pairs invariantly with every <contravariant vector>, coefficient comparison forces the <covector> transformation law for that array.
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