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Skew-Hermitian matrix : ウィキペディア英語版
Skew-Hermitian matrix
In linear algebra, a square matrix with complex entries is said to be skew-Hermitian or antihermitian if its conjugate transpose is equal to its negative.〔, §4.1.1; , §3.2〕 That is, the matrix ''A'' is skew-Hermitian if it satisfies the relation
:A^\dagger = -A,\;
where \dagger denotes the conjugate transpose of a matrix. In component form, this means that
:a_ = -\overline{a_{j,i}},
for all ''i'' and ''j'', where ''a''''i'',''j'' is the ''i'',''j''-th entry of ''A'', and the overline denotes complex conjugation.
Skew-Hermitian matrices can be understood as the complex versions of real skew-symmetric matrices, or as the matrix analogue of the purely imaginary numbers.〔, §4.1.2〕 All skew-Hermitian n×n matrices form the u(n) Lie algebra, which corresponds to the Lie group U(n).
The concept can be generalized to include linear transformations of any complex vector space with a sesquilinear norm.
== Example 1 ==

For example, the following matrix is skew-Hermitian:
:\begin 0 & 2 + i \\ -(2 - i) & 0 \end

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