We'd like to use analytics cookies to understand which symbols people look up, so we know what to research next. They are not used for advertising and we set none of them unless you say yes. What we store.
A lowercase epsilon with three indices, valued minus one, zero or one.
Also known as: Permutation symbol, Antisymmetric symbol, Alternating symbol
Sometimes confused with: Epsilon tensor
The Levi-Civita symbol is defined by a rule about swaps rather than a table of values: it is 1 for an even permutation of its indices, minus 1 for an odd one, and 0 if any index repeats. That single rule is what makes the cross product and the determinant expressible in one line each.
Denotes the totally antisymmetric symbol taking value 1, −1 or 0 according to the parity of its index permutation.
Contexts: Mathematics
Expresses the cross product and the determinant compactly under the summation convention, which is its main working use.
Contexts: Mathematics
Is a symbol rather than a tensor in general coordinates; the corresponding tensor carries a metric determinant factor.
Contexts: Mathematics
A lowercase Greek epsilon, a small curve open to the right, carrying three small index letters.