On the Unitary Diagonalisation of a Special Class of Quaternion Matrices

Authors

Clive Cheong Took, Imperial College
Danilo P. Mandic, Imperial College
Fuzhen Zhang, Nova Southeastern UniversityFollow

Document Type

Article

Publication Date

11-1-2011

Publication Title

Applied Mathematics Letters

Keywords

Takagi factorisation, Quaternion involutions, Unitary diagonalisation, Augmented quaternion statistics

ISSN

0893-9659

Volume

24

Issue/No.

11

First Page

1806

Last Page

1809

Abstract

We propose a unitary diagonalisation of a special class of quaternion matrices, the so-called ηη-Hermitian matrices A = A^ηH , η∈{ı,J,K} arising in widely linear modelling. In 1915, Autonne exploited the symmetric structure of a matrix A = A^T to propose its corresponding factorisation (also known as the Takagi factorisation) in the complex domain C. Similarly, we address the factorisation of an ‘augmented’ class of quaternion matrices, by taking advantage of their structures unique to the quaternion domain H. Applications of such unitary diagonalisation include independent component analysis and convergence analysis in statistical signal processing.

NSUWorks Citation

Took, Clive Cheong; Mandic, Danilo P.; and Zhang, Fuzhen, "On the Unitary Diagonalisation of a Special Class of Quaternion Matrices" (2011). Mathematics Faculty Articles. 94.
https://nsuworks.nova.edu/math_facarticles/94

DOI

10.1016/j.aml.2011.04.038