Abstract
<p> We propose a unitary diagonalisation of a special class of quaternion matrices, the so-called ηη-Hermitian matrices <strong> A </strong> = <strong> A </strong> <sup> η <em> H </em> </sup> , η∈{ <em> ı </em> , <em> J </em> , <em> K </em> } arising in widely linear modelling. In 1915, Autonne exploited the symmetric structure of a matrix <strong> A </strong> = <strong> A </strong> <em> <sup> T </sup> </em> to propose its corresponding factorisation (also known as the Takagi factorisation) in the complex domain <strong> C </strong> . Similarly, we address the factorisation of an ‘augmented’ class of quaternion matrices, by taking advantage of their structures unique to the quaternion domain <strong> H </strong> . Applications of such unitary diagonalisation include independent component analysis and convergence analysis in statistical signal processing.</p>
Original language | American English |
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Journal | Applied Mathematics Letters |
Volume | 24 |
DOIs | |
State | Published - Nov 1 2011 |
Keywords
- Augmented quaternion statistics
- Quaternion involutions
- Takagi factorisation
- Unitary diagonalisation
Disciplines
- Mathematics