The algebra of S2-upper triangular matrices.

Based on work presented in [S. R. Lippold, M. D. Staic and A. Stancu, Edge partitions of the complete graph and a determinant-like function, <italic>Monatsh. Math.</italic> <bold>198</bold> (2022) 819–858], we define S2-Upper Triangular Matrices and S2-Lower Triangular Matrices, two special types of d × d(2d − 1) matrices generalizing Upper and Lower Triangular Matrices, respectively. Then, we show that the property that the determinant of an Upper Triangular Matrix is the product of its diagonal entries is generalized under our construction. Further, we construct the algebra of S2-Upper Triangular Matrices and give conditions for an LU-Decomposition with S2-Lower Triangular and S2-Upper Triangular Matrices, respectively. [ABSTRACT FROM AUTHOR]