Antisymmetric matrix
An antisymmetric (or skew-symmetric) matrix is a matrix such that . In other words, a matrix is antisymmetric if it is equal to its negative transpose.
For example, the matrix
is anti-symmetric, because
.
Properties[change | change source]
- If you add two antisymmetric matrices, the result is another antisymmetric matrix.
- If you multiply an antisymmetric matrix by a constant, the result is another antisymmetric matrix.
- All of the diagonal entries of an antisymmetric matrix are 0.
Applications[change | change source]
For an electromagnetic field, the curvature form is an antisymmetric matrix whose elements are the electric field and magnetic field: the electromagnetic tensor.