4 papers
Enumeration of Laplacian integral and {-1,0,1}-diagonalizable graphs
Nathaniel Johnston, Sarah Plosker, Luis M. B. Varona
A graph with Laplacian matrix is called Laplacian integral if the eigenvalues of are all integers, and it is called -diagonalizable if has a full set of eig…
Approximating quantum states by states of low rank
Nathaniel Johnston, Chi-Kwong Li
Given a positive integer k, it is natural to ask for a formula for the distance between a given density matrix (i.e., mixed quantum state) and the set of density matrices of rank a…
Generalizing the Cauchy-Schwarz inequality: Hadamard powers and tensor products
Nathaniel Johnston, Sarah Plosker, Charles Torrance +1
We explore and generalize a Cauchy-Schwarz-type inequality originally proved in [Electronic Journal of Linear Algebra 35, 156-180 (2019)]: $\|\mathbf{v}^2\|\|\mathbf{w}^2\| - \lang…
The Factor Width Rank of a Matrix
Nathaniel Johnston, Shirin Moein, Sarah Plosker
A matrix is said to have factor width at most if it can be written as a sum of positive semidefinite matrices that are non-zero only in a single principal submatri…