Di Nola, Antonio; Sessa, Salvatore On the Schein rank of matrices over linear lattices. (English) Zbl 0668.15013 Linear Algebra Appl. 118, 155-158 (1989). The Schein rank of matrices over a linear lattice is the least number of rank 1 matrices \(u^ Tv\) whose sum is the given matrix. The authors prove that it can be attained by rank 1 matrices associated canonically with partitions of the set ṉ\(\times \underline m\) for \(n\times m\) matrices. Reviewer: K.H.Kim Cited in 1 Review MSC: 15B48 Positive matrices and their generalizations; cones of matrices 15A03 Vector spaces, linear dependence, rank, lineability 15B36 Matrices of integers 05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.) Keywords:matrices over linear lattices; fuzzy matrices; Schein rank; rank 1 matrices; partitions PDFBibTeX XMLCite \textit{A. Di Nola} and \textit{S. Sessa}, Linear Algebra Appl. 118, 155--158 (1989; Zbl 0668.15013) Full Text: DOI References: [1] Di Nola, A.; Pedrycz, W.; Sessa, S., When is a fuzzy relation decomposable in two fuzzy sets?, Fuzzy Sets and Systems, 16, 87-90 (1985) · Zbl 0576.08001 [2] Kim, K. H., Boolean Matrix Theory and Applications (1982), Marcel Dekker: Marcel Dekker New York [3] Kim, K. H.; Roush, F., Generalized fuzzy matrices, Fuzzy Sets and Systems, 4, 293-315 (1980) · Zbl 0451.20055 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.