Category:Definitions/Polar Decompositions

This category contains definitions related to Polar Decompositions.
Related results can be found in Category:Polar Decompositions.

Let $\mathbf A$ be a square matrix over the complex numbers.

A polar decomposition of $\mathbf A$ is a factorization of $\mathbf A$ in the form:

$\mathbf A = \mathbf {U H}$

where:

$\mathbf U$ is a unitary matrix

$\mathbf H$ is a Hermitian matrix with non-negative eigenvalues.