Involve: A Journal of Mathematics

  • Involve
  • Volume 10, Number 5 (2017), 781-799.

Matrix completions for linear matrix equations

Geoffrey Buhl, Elijah Cronk, Rosa Moreno, Kirsten Morris, Dianne Pedroza, and Jack Ryan

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Abstract

A matrix completion problem asks whether a partial matrix composed of specified and unspecified entries can be completed to satisfy a given property. This work focuses on determining which patterns of specified and unspecified entries correspond to partial matrices that can be completed to solve three different matrix equations. We approach this problem with two techniques: converting the matrix equations into linear equations and examining bases for the solution spaces of the matrix equations. We determine whether a particular pattern can be written as a linear combination of the basis elements. This work classifies patterns as admissible or inadmissible based on the ability of their corresponding partial matrices to be completed to satisfy the matrix equation. Our results present a partial or complete characterization of the admissibility of patterns for three homogeneous linear matrix equations.

Article information

Source
Involve, Volume 10, Number 5 (2017), 781-799.

Dates
Received: 22 November 2015
Revised: 14 June 2016
Accepted: 6 October 2016
First available in Project Euclid: 19 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1508433092

Digital Object Identifier
doi:10.2140/involve.2017.10.781

Mathematical Reviews number (MathSciNet)
MR3652447

Zentralblatt MATH identifier
1364.15021

Subjects
Primary: 15A83: Matrix completion problems
Secondary: 15A27: Commutativity

Keywords
matrix completion problems partial matrices matrix commutativity matrix equations

Citation

Buhl, Geoffrey; Cronk, Elijah; Moreno, Rosa; Morris, Kirsten; Pedroza, Dianne; Ryan, Jack. Matrix completions for linear matrix equations. Involve 10 (2017), no. 5, 781--799. doi:10.2140/involve.2017.10.781. https://projecteuclid.org/euclid.involve/1508433092


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