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Iwasawa decomposition (Theorem)

Let $ A$ be an invertible matrix with real coefficients. Then there exist unique matrices $ O$, $ D$, $ U$, such that

  1. $ A=ODU$.
  2. $ O$ is an orthogonal matrix.
  3. $ D$ is a diagonal matrix with positive diagonal entries.
  4. $ U$ is a unit upper triangular matrix.



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See Also: matrix factorization
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Cross-references: unit upper triangular matrix, diagonal, positive, diagonal matrix, orthogonal matrix, coefficients, real, matrix, invertible
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This is version 4 of Iwasawa decomposition, born on 2004-08-09, modified 2004-08-10.
Object id is 6088, canonical name is IsawasaDecomposition.
Accessed 4566 times total.

Classification:
AMS MSC: 15A99 (Linear and multilinear algebra; matrix theory :: Miscellaneous topics)
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