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These row operations and the elementary bidiagonal factorization of totally nonnegative matrices assist us in generalizing the inequalities by Gantmacher-Krein (1941) for these matrices. This further unravels a parallel essence regarding the matrix identities due to Karlin (1968) and due to Laplace (1772) for totally nonnegative matrices.

These refinements reveal an analogous underlying pattern: a sequence of inequalities oscillating about zero. This intrigued us to investigate if more such inequalities exist for totally nonnegative matrices. Using the identification of these matrices with planar networks and the inequality-preserving row operations introduced above, we obtain a novel class of these oscillating inequalities.

# Department Colloquium

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Fri., Mar. 3, 2023 3:30 p.m.
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Location: RIC 208
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**Speaker:** Prateek Vishwakarma, University of Regina

**Title: **Identities and inequalities for totally nonnegative matrices: Gantmacher-Krein, Karlin, and Laplace (85 kB)

**Abstract: **

These row operations and the elementary bidiagonal factorization of totally nonnegative matrices assist us in generalizing the inequalities by Gantmacher-Krein (1941) for these matrices. This further unravels a parallel essence regarding the matrix identities due to Karlin (1968) and due to Laplace (1772) for totally nonnegative matrices.

These refinements reveal an analogous underlying pattern: a sequence of inequalities oscillating about zero. This intrigued us to investigate if more such inequalities exist for totally nonnegative matrices. Using the identification of these matrices with planar networks and the inequality-preserving row operations introduced above, we obtain a novel class of these oscillating inequalities.