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math.CO2025
On the Maximum Spread of Non-Negative Matrices
Susie Lu, John Urschel
Given a directed graph , the spread of is the largest distance between any two eigenvalues of its adjacency matrix. In 2022, Breen, Riasanovsky, Tait, and Urschel asked what…
math.CO2024
On the Frobenius norm of the inverse of a non-negative matrix
Elsa Frankel, John Urschel
We prove a new lower bound for the Frobenius norm of the inverse of an non-negative matrix. This bound is only a modest improvement over previous results, but is sufficient for ful…
math.CO2024
Recovering a Magnitude-Symmetric Matrix from its Principal Minors
Victor-Emmanuel Brunel, John Urschel
We consider the inverse problem of finding a magnitude-symmetric matrix (matrix with opposing off-diagonal entries equal in magnitude) with a prescribed set of principal minors. Th…