In linear algebra, a square matrix (or more generally, a linear transformation from a complex vector space with a sesquilinear norm to itself) A is said to be skew-Hermitian or antihermitian if its conjugate transpose A^* is also its negative. That is, if it satisfies the relation:

A^* = −A

or in component form, if A = (a_i,j):

for all i and j.

Examples

For example, the following matrix is skew-Hermitian:

Properties

All entries on the main diagonal of a skew-Hermitian matrix have to be pure imaginary.

See also

• skew-symmetric matrix
• Hermitian matrix
• normal matrix
• unitary matrix.