Existence, Uniqueness, and Utility of an Analytic Parahermitian Matrix EVD

Dr. Stephan Alexander Weiss | April 26, 2017 | 14:00 | B04, L4101

Abstract

The eigenvalue decomposition of a Hermitian matrix has favourable properties, which have been exploited for a variety of optimal solutions to narrowband problems. We will explore the extension to space-time covariance matrices that can capture the 2nd order statistics of broadband problems; their z-transform has a parahermitian structure, which extends the Hermitian property to matrices of functions. To investigate such a parahermitian matrix EVD,  first we will look towards the unit circle via an analytic EVD, before we investigate off the unit-circle with the ultimate aim to establish a time-domain solution. We will gain some insight into the problems and feasibility  of established polynomial matrix EVD algorithms, that despite a number of successful algorithms with proven convergence tend to result in high-order factorisations. I will conclude by showing some toy problems where a polynomial approach admits simple solutions that a Fourier approach cannot yield.

Bio

WeissI am a Reader at the University of Strathclyde (Glasgow, Scotland), and head the Centre for Signal and Image Processing (7 academic staff and some 40 researchers and PhD students). The above topic is closely tied to my homes: Scotland through the work of Colin MacLaurin, and Germany through Karl Weierstrass‘ and Franz Rellich’s contributions.

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