A structure-preserving QR factorization for centrosymmetric real matrices Konrad Burnik University of Zagreb, Croatia Abstract We construct a QR factorization of a given centrosymmetric real matrix A into centrosymmetric real matrices Q and R. We describe in detail a Householder-type algorithm based on perplectic orthogonal block-reﬂectors to obtain such a factorization and demonstrate an application of this result to solving centrosymmetric linear systems of full rank. Keywords: perplectic, centrosymmetric, block-reﬂectors, QR factorization, structure-preserving Copyright c  2015 by Konrad Burnik. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ The ﬁnal version published by Elsevier can be found at http://dx.doi.org/10.1016/j.laa.2015.06.036 1. Introduction The aim of this paper is to describe a specialized QR factorization which arises from one particular indeﬁnite scalar product: the perplectic scalar product. In this section we shall give an informal description of the reasoning that led to our main result. The detailed formal treatment will be given in subsequent sections. Email address: kburnik@gmail.com (Konrad Burnik) Preprint submitted to Elsevier April 7, 2013