On Solutions of the Matrix Equation A∘lX = B with respect to MM-2 Semitensor Product

On Solutions of the Matrix Equation A∘lX = B with respect to MM-2 Semitensor Product

MM-2 semitensor product is a new and very useful mathematical tool, which breaks the limitation of traditional matrix multiplication on the dimension of matrices and has a wide application prospect. This article aims to investigate the solutions of the matrix equation A°lX=B with respect to MM-2 sem...

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Main Author: Jin Wang
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2021/6651434
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spelling doaj-1269989c484e4814a44bfb97516dbbc92021-03-08T02:01:33ZengHindawi LimitedJournal of Mathematics2314-47852021-01-01202110.1155/2021/6651434On Solutions of the Matrix Equation A∘lX = B with respect to MM-2 Semitensor ProductJin Wang0School of MathematicsMM-2 semitensor product is a new and very useful mathematical tool, which breaks the limitation of traditional matrix multiplication on the dimension of matrices and has a wide application prospect. This article aims to investigate the solutions of the matrix equation A°lX=B with respect to MM-2 semitensor product. The case where the solutions of the equation are vectors is discussed first. Compatible conditions of matrices and the necessary and sufficient condition for the solvability is studied successively. Furthermore, concrete methods of solving the equation are provided. Then, the case where the solutions of the equation are matrices is studied in a similar way. Finally, several examples are given to illustrate the efficiency of the results.http://dx.doi.org/10.1155/2021/6651434
collection DOAJ
language English
format Article
sources DOAJ
author Jin Wang
spellingShingle Jin Wang
On Solutions of the Matrix Equation A∘lX = B with respect to MM-2 Semitensor Product
Journal of Mathematics
author_facet Jin Wang
author_sort Jin Wang
title On Solutions of the Matrix Equation A∘lX = B with respect to MM-2 Semitensor Product
title_short On Solutions of the Matrix Equation A∘lX = B with respect to MM-2 Semitensor Product
title_full On Solutions of the Matrix Equation A∘lX = B with respect to MM-2 Semitensor Product
title_fullStr On Solutions of the Matrix Equation A∘lX = B with respect to MM-2 Semitensor Product
title_full_unstemmed On Solutions of the Matrix Equation A∘lX = B with respect to MM-2 Semitensor Product
title_sort on solutions of the matrix equation a∘lx = b with respect to mm-2 semitensor product
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4785
publishDate 2021-01-01
description MM-2 semitensor product is a new and very useful mathematical tool, which breaks the limitation of traditional matrix multiplication on the dimension of matrices and has a wide application prospect. This article aims to investigate the solutions of the matrix equation A°lX=B with respect to MM-2 semitensor product. The case where the solutions of the equation are vectors is discussed first. Compatible conditions of matrices and the necessary and sufficient condition for the solvability is studied successively. Furthermore, concrete methods of solving the equation are provided. Then, the case where the solutions of the equation are matrices is studied in a similar way. Finally, several examples are given to illustrate the efficiency of the results.
url http://dx.doi.org/10.1155/2021/6651434
work_keys_str_mv AT jinwang onsolutionsofthematrixequationalxbwithrespecttomm2semitensorproduct
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