Antisymmetric matrix

An antisymmetric (or skew-symmetric) matrix is a matrix formula_1 such that formula_2. In other words, a matrix is antisymmetric if it is equal to its negative transpose.
For example, the matrix
formula_3
is anti-symmetric, because
formula_4.
Applications.
For an electromagnetic field, the curvature form is an antisymmetric matrix whose elements are the electric field and magnetic field: the electromagnetic tensor.