||It has been suggested that this article be merged into Skew-Hermitian matrix. (Discuss) Proposed since June 2016.|
An by complex or real matrix is said to be anti-Hermitian, skew-Hermitian, or said to represent a skew-adjoint operator, or to be a skew-adjoint matrix, on the complex or real dimensional space , if its adjoint is the negative of itself: :.
Note that the adjoint of an operator depends on the scalar product considered on the dimensional complex or real space . If denotes the scalar product on , then saying is skew-adjoint means that for all one has
In the particular case of the canonical scalar products on , the matrix of a skew-adjoint operator satisfies for all .