Halmos College Presented Last Math Symposium for Fall 2019

On Friday, November 15, at 12pm, Edgar Pereia, Ph.D. presented his lecture entitled, “Minimal Rank Completions of Partial Matrices?”. Pereia is a professor at Federal University of Rio Grande do Norte, Natal, Brazil.

His lecture discussed Completion problems for partial matrices are defined and partial matrices are associated to bipartite graphs. Minimal ranks for scalar and block partial matrices with simple structures are presented. Calculating the minimal rank is classified as an NP-hard problem, what means that in general it is very difficult to calculate the minimal rank of an unstructured block (scalar) partial matrix. A conjecture states that the minimal rank of a partial matrix has an exact formula if and only if the associated bipartite graph is chordal. We present some upper estimates for the case that the associated bipartite graph is a single cycle, the most simple non-chordal case. The symmetric cyclic case is also treated.

Halmos College of Natural Sciences and Oceanography department of mathematics hosts the mathematics colloquium series in Parker Building, Room 338. For more information about the math colloquium series, please contact mathematics faculty member Jing Chen, Ph.D. jchen1@nova.edu or Evan Haskell haskell@nova.edu.