Displacement Rank of Generalized Inverses of Persymmetric Matrices
Pierre Comon, Pascal Laurent-Gengoux · SIAM Journal on Matrix Analysis and Applications · 1993
Toeplitz matrices are persymmetric matrices belonging to the large class of so-called structured matrices, characterized by their displacement rank. This characterization was introduced 12 years ago by Kailath and others. In this framework, properties of singular structured persymmetric matrices are investigated with the goal of proving the possible existence of fast algorithms for computing their pseudo-inverses. Loosely speaking, it is proved that the pseudo-inverses of some structured matrices with displacement rank r have a displacement rank bounded by $2r$.