On the Unitary Diagonalisation of a Special Class of Quaternion Matrices

Clive Cheong Took, Danilo P. Mandic, Fuzhen Zhang

Research output: Contribution to journalArticlepeer-review

Abstract

<p> We propose a unitary diagonalisation of a special class of quaternion matrices, the so-called &eta;&eta;-Hermitian matrices <strong> A </strong> = <strong> A </strong> <sup> &eta; <em> H </em> </sup> , &eta;&isin;{ <em> &inodot; </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 &lsquo;augmented&rsquo; 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 languageAmerican English
JournalApplied Mathematics Letters
Volume24
DOIs
StatePublished - Nov 1 2011

Keywords

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

Disciplines

  • Mathematics

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