Factorization of Unitary Matrices

TL;DR

This paper presents a novel factorization method for unitary matrices, expressing them as products of phase-diagonal and orthogonal matrices, along with an explicit Weyl factorization.

Contribution

It introduces a new factorization approach for unitary matrices involving diagonal phase matrices and orthogonal matrices, including an explicit Weyl form.

Findings

Explicit factorization of unitary matrices into phases and orthogonal matrices

Derivation of an explicit Weyl factorization form

Provides a constructive method for matrix decomposition

Abstract

Factorization of an $n\times n$ unitary matrix as a product of $n$ diagonal matrices containing only phases interlaced with $n-1$ orthogonal matrices each one generated by a real vector as well as an explicit form for the Weyl factorization are found.