 Tensor component transformation law

ID: tensor-component-transformation-law

Under a coordinate change

x \mapsto x^{'}

, the components of a type-

(r, s)

tensor acquire one forward Jacobian for each contravariant index and one inverse Jacobian for each covariant index. For a type-

(1, 1)

T^{μ^{'}}_{ν^{'}} = \frac{\partial x ^{μ^{'}}}{\partial x ^{α}} \frac{\partial x ^{β}}{\partial x ^{ν^{'}}} T^{α}_{β} .

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