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In mathematics, the Bruhat decomposition (introduced by François Bruhat for classical groups and by Claude Chevalley in general) G = BWB into cells can be regarded as a general expression of the principle of Gauss–Jordan elimination, which generically writes a matrix as a product of an upper triangular and lower triangular matrices—but with exceptional cases. It is related to the Schubert cell decomposition of Grassmannians: see Weyl group for this. More generally, any group with a (B,N) pair has a Bruhat decomposition. ==Definitions== *''G'' is a connected, reductive algebraic group over an algebraically closed field. *''B'' is a Borel subgroup of ''G'' *''W'' is a Weyl group of ''G'' corresponding to a maximal torus of ''B''. The Bruhat decomposition of ''G'' is the decomposition : of ''G'' as a disjoint union of double cosets of ''B'' parameterized by the elements of the Weyl group ''W''. (Note that although ''W'' is not in general a subgroup of ''G'', the coset ''wB'' is still well defined.) 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「Bruhat decomposition」の詳細全文を読む スポンサード リンク
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