Pressman, Irwin S. Matrices with multiple symmetry properties: applications of centro-Hermitian and per-Hermitian matrices. (English) Zbl 0957.15019 Linear Algebra Appl. 284, No. 1-3, 239-258 (1998). In this paper the authors introduce three matrix patterns, essentially asking that the matrix is either real or pure imaginary or zero, that combined with the twelve known symmetric patterns (symmetric, centrosymmetric, persymmetric, Hermitian, centro-Hermitian, per-Hermitian, skew-symmetric, skew-centrosymmetric, skew-persymmetric, skew-Hermitian, skew-centro-Hermitian, skew-per-Hermitian) form a Steiner triple system.In addition, using a group of operators on the linear group over the complex numbers they reach types of matrices that satisfy sets of patterns, and that yield to unique decompositions into matrices of the same type. 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