Centrosymmetric and centro-skewsymmetric Toeplitz-plus-Hankel matrices and Bézoutians
The present paper can be seen as a continuation of the authors' paper [ibid. 343-344, 195-209 (2002; Zbl 0995.15022)]. However, now Toeplitz matrices which are at the same time Hankel (shortly: T + H matrices) are considered, and for centrosymmetric [centro-skewsymmetric] matrices of this type algebraic properties are investigated. One of the main results is concerned with the inversion of regular centrosymmetric [centro-skewsymmetric] T + H matrices. The inverse of such a matrix can be represented with the help of some special, simply structured T + H Bézoutian. For singular matrices of this kind the structure of the kernel is described in terms of the related Toeplitz system. Furthermore, centrosymmetric [centro-skewsymmetric] T + H Bézoutians are characterized: General centrosymmetric [centro-skewsymmetric] T + H Bézoutians can be represented as the sum of two special T + H Bézoutians which can be reduced to Hankel Bézoutians of about half their size.
scientific article; zbMATH DE number 1915808