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On the Schein rank of matrices over linear lattices. (English) Zbl 0668.15013

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

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.)
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References:

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