Matrix completions for linear matrix equations
| Autor: | Elijah Cronk, Dianne Pedroza, Geoffrey Buhl, Jack Ryan, Rosa K. Moreno, Kirsten Morris |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
matrix commutativity
15A27 partial matrices General Mathematics 010102 general mathematics 010103 numerical & computational mathematics Single-entry matrix 01 natural sciences Square matrix Augmented matrix Algebra matrix completion problems Matrix (mathematics) matrix equations Matrix splitting 15A83 Symmetric matrix Nonnegative matrix 0101 mathematics Coefficient matrix Mathematics |
| Zdroj: | Involve 10, no. 5 (2017), 781-799 |
| ISSN: | 1944-4184 1944-4176 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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