# Iwasawa decomposition

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

1. 1.

$A=ODU$.

2. 2.

$O$ is an orthogonal matrix.

3. 3.

$D$ is a diagonal matrix with positive diagonal entries.

4. 4.

$U$ is a unit upper triangular matrix.

Title Iwasawa decomposition IwasawaDecomposition 2013-03-22 14:32:29 2013-03-22 14:32:29 mathwizard (128) mathwizard (128) 7 mathwizard (128) Theorem msc 15A99 MatrixFactorization