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Birkhoff decomposition

Topics referred to by the same term

Birkhoff decomposition refers to two different mathematical concepts:

  • The Birkhoff factorization, introduced by George David Birkhoff at 1909, is the presentation of an invertible matrix with polynomial coefficients as a product of three matrices.
  • The Birkhoff - von Neumann decomposition, introduced by Garrett Birkhoff (George's son) at 1946, is the presentation of a bistochastic matrix as a convex sum of permutation matrices. It can be found by the Birkhoff algorithm.
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This article is adapted from the Wikipedia article Birkhoff decomposition, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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