The Cauchy stress tensor obeys the tensor transformation law under a change in the system of coordinates.
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The field tensor derives its name from the fact that the electromagnetic field is found to obey the tensor transformation law, this general property of ( non-gravitational ) physical laws being recognised after the advent of special relativity.
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Both equations can also be obtained by applying the tensor transformation law on the known Cauchy stress tensor, which is equivalent to performing the static equilibrium of forces in the direction of \ sigma _ \ mathrm { n } and \ tau _ \ mathrm { n }.
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