TITLE:
Solution of the Matrix Second Semi-Tensor Product Equation A ∘ l X ∘ l B=C
AUTHORS:
Hao Zhang
KEYWORDS:
Matrix Equation, The Second Semi-Tensor Product, Compatibility Condition, Sufficient and Necessary Conditions, Vectorization
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.10,
October
8,
2024
ABSTRACT: In this paper, the solution of the matrix second semi-tensor product equation
A
∘
l
X
∘
l
B=C
is studied. Firstly, the solvability of the matrix-vector second semi-tensor product equation is investigated. At the same time, the compatibility conditions, the sufficient and necessary conditions and the specific solution methods for the matrix solution are given. Secondly, we further consider the solvability of the second semi-tensor product equation of the matrix. For each part, several examples are given to illustrate the validity of the results.