A structure-preserving QR factorization for centrosymmetric real matrices

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.