On Solutions of the Matrix Equation  A   ∘   l   X  = B with respect to  M M -2 Semitensor Product | Zendy

Jin Wang | Zendy

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On Solutions of the Matrix Equation

A \circ_{l} X

= B with respect to

M M

-2 Semitensor Product

Author(s) -

Jin Wang

Publication year - 2021

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2021/6651434

Subject(s) - mathematics , matrix (chemical analysis) , product (mathematics) , dimension (graph theory) , matrix multiplication , algebra over a field , combinatorics , pure mathematics , geometry , physics , materials science , composite material , quantum , quantum mechanics

M M -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 ° l X = B with respect to M M -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.

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