|
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 : where denotes the conjugate transpose of a matrix. In component form, this means that : 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: : 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Skew-Hermitian matrix」の詳細全文を読む スポンサード リンク
|