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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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

matrix completion problems partial matrices matrix commutativity matrix equations


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.

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