Steele, A.; Yalim, J.; Welfert, B. QX factorization of centrosymmetric matrices. (English) Zbl 1400.15016 Appl. Numer. Math. 134, 11-16 (2018). Summary: We show how the factorization \(A = Q X\), introduced in [K. Burnik, Linear Algebra Appl. 484, 356–378 (2015; Zbl 1327.15076)], of a real centrosymmetric \(m \times n\) matrix \(A\) into a centrosymmetric orthogonal \(m \times m\) matrix \(Q\) and a centrosymmetric \(m \times n\) matrix \(X\) with a double-cone structure can be directly obtained via standard QR factorizations of two matrices about half the size of \(A\). Examples and a Matlab code are included. Cited in 2 Documents MSC: 15A23 Factorization of matrices 15B57 Hermitian, skew-Hermitian, and related matrices 65F30 Other matrix algorithms (MSC2010) Keywords:centrosymmetry; QR factorization Citations:Zbl 1327.15076 Software:Matlab PDFBibTeX XMLCite \textit{A. Steele} et al., Appl. Numer. Math. 134, 11--16 (2018; Zbl 1400.15016) Full Text: DOI References: [1] Andrew, A. L., Eigenvectors of certain matrices, Linear Algebra Appl., 7, 157-162, (1973) · Zbl 0255.65021 [2] Burnik, K., A structure-preserving QR factorization for centrosymmetric real matrices, Linear Algebra Appl., 484, 356-378, (2015) · Zbl 1327.15076 [3] Datta, L.; Morgera, S. D., On the reducibility of centrosymmetric matrices - applications in engineering problems, Circuits Syst. Signal Process., 8, 71-96, (1989) · Zbl 0674.15005 [4] Godd, I. J., The inverse of a centrosymmetric matrix, Technometrics, 12, 925-928, (1970) · Zbl 0194.05903 [5] Mackey, D. S.; Mackey, N.; Dunlavy, D. M., Structure preserving algorithms for perplectic eigenproblems, Electron. J. Linear Algebra, 13, (2005), article 2 · Zbl 1065.65053 [6] Weaver, J. R., Centrosymmetric (cross-symmetric) matrices, their basic properties, eigenvalues, and eigenvectors, Am. Math. Mon., 92, 711-717, (1985) · Zbl 0619.15021 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.