590 citations · 1.7k across the 45 of their papers we have counts for
45 papers
Laplacian - and -diagonalizable graphs
Nathaniel Johnston, Sarah Plosker
A graph is called "Laplacian integral" if the eigenvalues of its Laplacian matrix are all integers. We investigate the subset of these graphs whose Laplacian is furthermore diagona…
A New Formula for the Determinant and Bounds on Its Tensor and Waring Ranks
Robin Houston, Adam P. Goucher, Nathaniel Johnston
We present a new explicit formula for the determinant that contains superexponentially fewer terms than the usual Leibniz formula. As an immediate corollary of our formula, we show…
Bounding Real Tensor Optimizations via the Numerical Range
Nathaniel Johnston, Logan Pipes
We show how the numerical range of a matrix can be used to bound the optimal value of certain optimization problems over real tensor product vectors. Our bound is stronger than the…
Computing linear sections of varieties: quantum entanglement, tensor decompositions and beyond
Nathaniel Johnston, Benjamin Lovitz, Aravindan Vijayaraghavan
We study the problem of finding elements in the intersection of an arbitrary conic variety in with a given linear subspace (where can be the real or com…
A Complete Hierarchy of Linear Systems for Certifying Quantum Entanglement of Subspaces
Nathaniel Johnston, Benjamin Lovitz, Aravindan Vijayaraghavan
We introduce a hierarchy of linear systems for showing that a given subspace of pure quantum states is entangled (i.e., contains no product states). This hierarchy outperforms know…
Real Schur norms and Hadamard matrices
John Holbrook, Nathaniel Johnston, Jean-Pierre Schoch
We present a preliminary study of Schur norms , where M is a matrix whose entries are , and denotes the entrywise (i.e., Sch…