3 papers
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-ph2024
Average Nodal Count and the Nodal Count Condition for Graphs
Lior Alon, John Urschel
The nodal edge count of an eigenvector of the Laplacian of a graph is the number of edges on which it changes sign. This quantity extends to any real symmetric matrix s…
cs.DS2023
Estimating the matrix norm
Larry Guth, Dominique Maldague, John Urschel
The matrix norm is a fundamental quantity appearing in a variety of areas of mathematics. This quantity is known to be efficiently computable in only a few specia…