Levi-Civita symbol
equals on even permutations of , on odd permutations, and when any two indices coincide.
Properties
The Levi-Civita symbol is antisymmetric and encodes cross products in an orthonormal right-handed basis:
Contraction identities
The full contraction identity expands products of two epsilons into Kronecker deltas:
Contracting indices gives the workhorse forms
Related
Stated in
- Definition 2.32 (Levi-Civita Epsilon)§2.7 Index Notation & Summation Conventions