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Let [tex]A^{ik}[/tex] be an antisymmetric tensor of rank 2; Why is [tex]A^{*ik}=1/2e ^{iklm}A_{lm}[/tex] defined its dual? [tex]e^{iklm}[/tex] is the completely antisymmetric unit tensor.

Furthermore, [tex]e^{iklm}[/tex] is a pseutotensor, what does it mean? Conversely, why the product [tex]e^{iklm} e_{prst}[/tex] is a true tensor?

Thanks in advance... ;)

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# [Special relativity - Mathematical background] Tensor and pseudo-tensor

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