Reconstructing matrices from minors

Charles R. Johnson, Joshua J. Mollner, Ashlyn M. Winkler

Research output: Contribution to journalArticlepeer-review

Abstract

Which collections of mn minors of an m-by-n matrix uniquely determine the matrix, given some regularity conditions? For m=n=3, the 585 such collections, that are distinct up to symmetry, are determined. For general m, n, a necessary and a sufficient condition for reconstruction are given in terms of matchings in a bipartite graph. Among other particular results, those collections of entries for which there are minors that permit reconstruction one entry at a time are characterized.

Original languageEnglish (US)
Pages (from-to)1733-1744
Number of pages12
JournalLinear Algebra and Its Applications
Volume434
Issue number7
DOIs
StatePublished - Apr 1 2011

Keywords

  • Arrangement bipartite graph
  • Configuration bipartite graph
  • Entry-wise sequential reconstruction
  • Reconstruction of matrices from minors
  • Unique reconstruction set

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

Fingerprint Dive into the research topics of 'Reconstructing matrices from minors'. Together they form a unique fingerprint.

Cite this