17th Annual Student Research Conference
Mathematics and Computer Science
Minimum Rank of Positive Semi-Definite Matrices with a Prescribed Graph
Kelly J. Steinmetz
Dr. Sivaram K. Narayan (Central Michigan University) and Dr. Upendra Kulkarni, Faculty Mentors
A complex nxn matrix A = [aij] is said to be combinatorially symmetric if for i ≠ j, aij ≠ 0 implies aji ≠ 0. We associate a simple graph G to a combinatorially symmetric matrix A such that V(G) = {1, 2, …, n} and join vertices i and j if and only if aij ≠ 0. The graph is independent of the diagonal entries of A. Define P(G) to be the class of all positive semi-definite matrices associated with a given graph G. Denote #(G) = min {rank A | A ε P(G) } the minimum PSD rank of G. In this talk I will present results about the minimum PSD rank of certain classes of graphs, including some very exciting recent results.
Keywords: Linear Algebra, Matrices, Eigenvalues, Graph, Symmetric, Semi-Definite, Rank
Topic(s):Mathematics
Presentation Type: Oral Paper
Session: 9-2
Location: VH 1232
Time: 8:45