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Matrix
completions for linear matrix equations
Geoffrey Buhl, Elijah Cronk, Rosa Moreno, Kirsten Morris, Dianne Pedroza and Jack Ryan
Vol. 10 (2017), No. 5, 781–799
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Abstract |
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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. |
Keywords
matrix completion problems, partial matrices, matrix
commutativity, matrix equations
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Mathematical Subject Classification 2010
Primary: 15A83
Secondary: 15A27
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Milestones
Received: 22 November 2015
Revised: 14 June 2016
Accepted: 6 October 2016
Published: 14 May 2017
Communicated by Chi-Kwong Li
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Authors |
| Geoffrey Buhl | |
| Department of Mathematics CA State Univ Channel Islands 1 University Dr. Camarillo, CA 93012 United States |
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| Elijah Cronk | |
| Department of Mathematics Ithaca College 953 Danby Rd. Ithaca, NY 14850 United States |
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| Rosa Moreno | |
| Department of Mathematics California State University Channel Islands 1 University Dr. Camarillo, CA 93012 United States |
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| Kirsten Morris | |
| Department of Mathematics The University of Georgia University of Georgia Athens, GA 30602 United States |
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| Dianne Pedroza | |
| Department of Mathematics Ripon College 300 Seward St. Ripon, WI 54971 United States |
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| Jack Ryan | |
| Department of Mathematics The University of Tennessee Knoxville 1403 Circle Dr. Knoxville, TN 37996 United States |
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