Definition:Polar Decomposition

Definition

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.

Also see

• Results about polar decompositions can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): factorization: 2. (of a matrix)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): polar decomposition
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): factorization: 2. (of a matrix)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): polar decomposition