2004 Student Research Conference:
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 ij, 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


Presentation Type: Oral Paper

Session: 9-2
Location: VH 1232
Time: 8:45

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