Title

Reconstructing matrices from minors

Document Type

Article

Department/Program

Mathematics

Journal Title

Linear Algebra and Its Applications

Pub Date

2011

Volume

434

Issue

7

First Page

1733

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. (C) 2010 Elsevier Inc. All rights reserved.

DOI

10.1016/j.laa.2010.09.018

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