Positive Semidefinite Matrix Factorizations
Kristen Dawson
Department of Mathematics
Faculty Supervisor: Serkan Hosten
A positive semidefinite (psd) factorization of a nonnegative matrix M expresses each entry of M as the inner product of two psd matrices. These factorizations correspond to spectrahedral lifts of a polytope associated with M. Our work utilizes tools from rigidity theory to characterize the uniqueness of a psd factorization of a matrix of rank 3 using psd matrices of size 2.