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- W2021000796 abstract "An m-by-n matrix A is said to be totally nonnegative if every minor of A is nonnegative. Our main interest lies in characterizing all the inequalities that exist among products of principal minors of totally nonnegative matrices. We provide a complete description of all such inequalities for n-by-n totally nonnegative matrices with n⩽5. Other general results are also proved including a characterization when detA[α1]detA[α2]⩽detA[β1]detA[β2], for index sets α1,α2,β1,β2, and A totally nonnegative, along with various set-theoretic operations that preserve inequalities with respect to the totally nonnegative matrices. Many aspects of bidiagonal factorizations for totally nonnegative matrices are employed throughout." @default.
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- W2021000796 date "2003-04-01" @default.
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- W2021000796 title "Multiplicative principal-minor inequalities for totally nonnegative matrices" @default.
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- W2021000796 doi "https://doi.org/10.1016/s0196-8858(02)00506-7" @default.
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