Antisymmetric matrix

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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.

Related pages[change | change source]