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Refined inertias of tree sign patterns of orders 2 and 3

Refined inertias of tree sign patterns of orders 2 and 3

Sign patterns are matrices with only the sign of each entry specified.The refined inertia of a matrix categorizes the eigenvalues as positive, negative, zero or nonzero imaginary, and the refined inertia of a sign pattern is the set of all refined inertias allowed by real matrices with that sign pattern.The …