Skew-Hermitian Matrix
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High Quality Content by WIKIPEDIA articles! 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.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_{i,j} = -overline{a_{j,i}}, for all i and j, where ai,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…mehr

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High Quality Content by WIKIPEDIA articles! 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.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_{i,j} = -overline{a_{j,i}}, for all i and j, where ai,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.The concept can be generalized to include linear transformations of any complex vector space with a sesquilinear norm.