📢Dual Anti-Symmetry of the Generalised Kronecker Delta

This is the demonstration of the dual anti-symmetry of the generalised Kronecker delta. Defined as a determinant, it is completely anti-symmetric in both its contravariant (upper) indices and its covariant (lower) indices. The derived relation, confirms that anti-symmetrising the covariant indices of the simple Kronecker delta product yields the generalised delta, mirroring the given result for contravariant index anti-symmetrisation. Crucially, the factor inherently present in the definition of the anti-symmetrisation operator, resulting in the determinant definition.

Proof of Covariant Index Anti-Symmetrisation | Proof and Derivationviadean on Notion