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2017 Matrix completions for linear matrix equations
Geoffrey Buhl, Elijah Cronk, Rosa Moreno, Kirsten Morris, Dianne Pedroza, Jack Ryan
Involve 10(5): 781-799 (2017). DOI: 10.2140/involve.2017.10.781

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.

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Geoffrey Buhl. Elijah Cronk. Rosa Moreno. Kirsten Morris. Dianne Pedroza. Jack Ryan. "Matrix completions for linear matrix equations." Involve 10 (5) 781 - 799, 2017. https://doi.org/10.2140/involve.2017.10.781

Information

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

zbMATH: 1364.15021
MathSciNet: MR3652447
Digital Object Identifier: 10.2140/involve.2017.10.781

Subjects:
Primary: 15A83
Secondary: 15A27

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.10 • No. 5 • 2017
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