# Minimal Rank Completions of Partial Matrices

## Description

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 a 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.

## Location

Parker Building, Room 338

Minimal Rank Completions of Partial Matrices

Parker Building, Room 338

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 a 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.

## Presenter Bio

Graduated in Bachelor of Mathematics from the Federal University of Rio Grande do Sul (1983) and PhD in Mathematics from the University of Beira Interior (2000). He is currently Reviewer of Applied Mathematics Letters, Associate Professor at Federal University of Rio Grande do Norte, Journal Reviewer of Applied Mathematics and Computation, Journal Reviewer of Automatica (Oxford), Journal Reviewer of Bulletin of the Korean Mathematical Society and Periodical Reviewer at Ecological Complexity (Print).