10.26165/JUELICH-DATA/BKJOES Di Napoli, Edoardo0000-0001-5821-5897(Forschungszentrum Jülich)Wu, Xinzhe0000-0001-5716-3116(Forschungszentrum Jülich) Jülich DATA 2026 Incremental dataset that includes algebraic matrices generated by a number of applications from Materials Science. The matrices are stored in a publicly accessible server. They can be easily accessed through a web interface 'MatrixHub' hosted on Github. The matrices can also be accessed directly by visiting the public server instead of accessing them through the MatrixHub interface. The purpose of this database of matrices is to provide medium to very large matrices to be utilized to benchmark numerical linear algebra routines. All matrices in the set have been generated with well-known and openly available simulation codes (see Software field). The matrix set includes Hermitian and pseudo-Hermitian square matrices of large sizes (from few thousands to hundreds of thousands). All the matrices represent Hamiltonians of quantum mechanical systems generated by either Density Functional Theory (DFT) methods or Bethe-Salpeter equation (BSE) methods. The matrices generated from BSE can be either Hermitian or pseudo-Hermitian. All matrices from DFT are Hermitian. Di Napoli, Edoardo(Forschungszentrum Jülich)Wu, Xinzhe(Forschungszentrum Jülich)Di Napoli, Edoardo(Forschungszentrum Jülich)Wu, Xinzhe(Forschungszentrum Jülich)Richefort, Clement(Forschungszentrum Jülich)Schleife, Andre(University of Illinois Urbana-Champaign)Ferretti, Andrea(Consiglio Nazionale delle Ricerche)