Iwasawa decomposition
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.
Title  Iwasawa decomposition 

Canonical name  IwasawaDecomposition 
Date of creation  20130322 14:32:29 
Last modified on  20130322 14:32:29 
Owner  mathwizard (128) 
Last modified by  mathwizard (128) 
Numerical id  7 
Author  mathwizard (128) 
Entry type  Theorem 
Classification  msc 15A99 
Related topic  MatrixFactorization 