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- Birkhoff_factorization abstract "In mathematics, Birkhoff factorization or Birkhoff decomposition, introduced by Birkhoff (1909), is the factorization of an invertible matrix M with coefficients that are Laurent polynomials in z into a product M = M+M0M−, where M+ has entries that are polynomials in z, M0 is diagonal, and M− has entries that are polynomials in z−1. There are several variations where the general linear group is replaced by some other reductive algebraic group, due to Grothendieck (1957).Birkhoff factorization implies the Birkhoff–Grothendieck theorem of Grothendieck (1957) that vector bundles over the projective line are sums of line bundles.Birkhoff factorization follows from the Bruhat decomposition for affine Kac-Moody groups (or loop groups), and conversely the Bruhat decomposition for the affine general linear group follows from Birkhoff factorization together with the Bruhat decomposition for the ordinary general linear group.".
- Birkhoff_factorization wikiPageExternalLink books?id=MbFBXyuxLKgC.
- Birkhoff_factorization wikiPageID "32023896".
- Birkhoff_factorization wikiPageLength "2211".
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- Birkhoff_factorization wikiPageRevisionID "546027977".
- Birkhoff_factorization wikiPageWikiLink American_Journal_of_Mathematics.
- Birkhoff_factorization wikiPageWikiLink Birkhoff–Grothendieck_theorem.
- Birkhoff_factorization wikiPageWikiLink Bruhat_decomposition.
- Birkhoff_factorization wikiPageWikiLink Category:Matrices.
- Birkhoff_factorization wikiPageWikiLink Line_bundle.
- Birkhoff_factorization wikiPageWikiLink Linear_group.
- Birkhoff_factorization wikiPageWikiLink Loop_group.
- Birkhoff_factorization wikiPageWikiLink Matrix_group.
- Birkhoff_factorization wikiPageWikiLink Transactions_of_the_American_Mathematical_Society.
- Birkhoff_factorization wikiPageWikiLink Vector_bundle.
- Birkhoff_factorization wikiPageWikiLinkText "Birkhoff factorization".
- Birkhoff_factorization authorlink "George David Birkhoff".
- Birkhoff_factorization first "G.".
- Birkhoff_factorization hasPhotoCollection Birkhoff_factorization.
- Birkhoff_factorization id "b/b120240".
- Birkhoff_factorization last "Birkhoff".
- Birkhoff_factorization last "Khimshiashvili".
- Birkhoff_factorization wikiPageUsesTemplate Template:Citation.
- Birkhoff_factorization wikiPageUsesTemplate Template:Eom.
- Birkhoff_factorization wikiPageUsesTemplate Template:Harvs.
- Birkhoff_factorization wikiPageUsesTemplate Template:Harvtxt.
- Birkhoff_factorization year "1090".
- Birkhoff_factorization year "1909".
- Birkhoff_factorization subject Category:Matrices.
- Birkhoff_factorization hypernym Factorization.
- Birkhoff_factorization type Matrix.
- Birkhoff_factorization comment "In mathematics, Birkhoff factorization or Birkhoff decomposition, introduced by Birkhoff (1909), is the factorization of an invertible matrix M with coefficients that are Laurent polynomials in z into a product M = M+M0M−, where M+ has entries that are polynomials in z, M0 is diagonal, and M− has entries that are polynomials in z−1.".
- Birkhoff_factorization label "Birkhoff factorization".
- Birkhoff_factorization sameAs m.0gx1307.
- Birkhoff_factorization sameAs Q4916481.
- Birkhoff_factorization sameAs Q4916481.
- Birkhoff_factorization wasDerivedFrom Birkhoff_factorization?oldid=546027977.
- Birkhoff_factorization isPrimaryTopicOf Birkhoff_factorization.