Ricci calculus
Kronecker delta

The Kronecker delta is like the identity matrix when multiplied and contracted:

The components δ are the same in any basis and form an invariant tensor of type (1, 1), i.e. the identity of the tangent bundle over the identity mapping of the base manifold, and so its trace is an invariant. Its trace is the dimensionality of the space; for example, in four-dimensional spacetime,

The Kronecker delta is one of the family of generalized Kronecker deltas. The generalized Kronecker delta of degree 2 p may be defined in terms of the Kronecker delta by (a common definition includes an additional multiplier of p ! on the right):

and acts as an antisymmetrizer on p indices:
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