On the unitary diagonalisation of a special class of quaternion matrices

We propose a unitary diagonalisation of a special class of quaternion matrices, the so-called η -Hermitian matrices A = A η H , η ∈ { ı , j , κ } 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.