Article
On the Unitary Diagonalisation of a Special Class of Quaternion Matrices
Applied Mathematics Letters
Document Type
Article
Publication Date
11-1-2011
Keywords
- Takagi factorisation,
- Quaternion involutions,
- Unitary diagonalisation,
- Augmented quaternion statistics
Disciplines
Abstract
We propose a unitary diagonalisation of a special class of quaternion matrices, the so-called ηη-Hermitian matrices A = AηH , η∈{ı,J,K} arising in widely linear modelling. In 1915, Autonne exploited the symmetric structure of a matrix A = AT 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.
DOI
10.1016/j.aml.2011.04.038
Citation Information
Clive Cheong Took, Danilo P. Mandic and Fuzhen Zhang. "On the Unitary Diagonalisation of a Special Class of Quaternion Matrices" Applied Mathematics Letters Vol. 24 Iss. 11 (2011) p. 1806 - 1809 ISSN: 0893-9659 Available at: http://works.bepress.com/fuzhen-zhang/110/