About: Skew-Hermitian matrix

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In linear algebra, a square matrix with complex entries is said to be skew-Hermitian or anti-Hermitian if its conjugate transpose is the negative of the original matrix. That is, the matrix is skew-Hermitian if it satisfies the relation where denotes the conjugate transpose of the matrix . In component form, this means that for all indices and , where is the element in the -th row and -th column of , and the overline denotes complex conjugation. Imaginary numbers can be thought of as skew-adjoint (since they are like matrices), whereas real numbers correspond to self-adjoint operators.

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rdfs:label	Skew-Hermitian matrix (en)
rdfs:comment	In linear algebra, a square matrix with complex entries is said to be skew-Hermitian or anti-Hermitian if its conjugate transpose is the negative of the original matrix. That is, the matrix is skew-Hermitian if it satisfies the relation where denotes the conjugate transpose of the matrix . In component form, this means that for all indices and , where is the element in the -th row and -th column of , and the overline denotes complex conjugation. Imaginary numbers can be thought of as skew-adjoint (since they are like matrices), whereas real numbers correspond to self-adjoint operators. (en)
sameAs	Skew-Hermitian matrix Skew-Hermitian matrix
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Equation_box_1 dbt:Short_description dbt:Tmath dbt:Matrix_classes
Subject	Abstract algebra Linear algebra Matrices
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Skew-Hermitian_matrix?oldid=1070319152&ns=0
Wikipage page ID	509788 (xsd:integer)
page length (characters) of wiki page	6204 (xsd:nonNegativeInteger)
Wikipage revision ID	1070319152 (xsd:integer)
has abstract	In linear algebra, a square matrix with complex entries is said to be skew-Hermitian or anti-Hermitian if its conjugate transpose is the negative of the original matrix. That is, the matrix is skew-Hermitian if it satisfies the relation where denotes the conjugate transpose of the matrix . In component form, this means that for all indices and , where is the element in the -th row and -th column of , 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 set of all skew-Hermitian matrices forms the 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. 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 . Imaginary numbers can be thought of as skew-adjoint (since they are like matrices), whereas real numbers correspond to self-adjoint operators. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Skew-Hermitian_matrix
is Wikipage redirect of	Skew-Hermitian Skew-Hermitian matrices Anti-Hermitian Anti-Hermitian matrix AntiHermitian Antihermitean Antihermitian Antihermitian matrix Skew-adjoint Skew-adjoint operator Skew-hermitian Skew Hermitian matrix
is Link from a Wikipage to another Wikipage of	List of things named after Charles Hermite Normal matrix Normal operator 3D rotation group Adjugate matrix Bivector (complex) Cayley transform Linear complex structure List of irreducible Tits indices List of linear algebra topics List of named matrices Complexification (Lie group) Compound matrix Conjugate transpose Hermitian Yang–Mills connection Hermitian matrix Gamma matrices Involutory matrix Lax pair Lie algebra Matrix decomposition Expm Matrix representation of Maxwell's equations Anti-Hermitian Anti-Hermitian matrix AntiHermitian Antihermitean Antihermitian Antihermitian matrix

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