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Products of M-matrices and nested sequences of principal minors

Products of M-matrices and nested sequences of principal minors

The question of whether or not the product of two nonsingular n-by-n M-matrices hasa nested sequence of positive principal minors (abbreviated to a nest) is considered. For n = 2, 3, 4such a product always has a nest, and this is conjectured for n = 5. For general n, examples …