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<p>In this paper, we examine the generalized column conjugate extension solution problem for matrix equations over quaternionic fields. Using the complex and real decompositions of quaternionic matrices and the structural characteristics of generalized conjugate extension matrices, the constrained quaternionic matrix equations are transformed into unconstrained equations over the real number field by means of the matrix Kronecker product, so as to obtain the sufficient conditions for the equations to have generalized columnar conjugate extension solutions as well as their generalized expressions, and then finally, the results are illustrated by numerical examples.</p>

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Generalized Conjugate Extension Solutions for Quaternionic Matrix Equations AX*B + CXD = E

  • 期刊论文

  • 发表日期：

    2025年9月12日

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  • Meng Huo,
  • Lan Zhang

摘要

In this paper, we examine the generalized column conjugate extension solution problem for matrix equations over quaternionic fields. Using the complex and real decompositions of quaternionic matrices and the structural characteristics of generalized conjugate extension matrices, the constrained quaternionic matrix equations are transformed into unconstrained equations over the real number field by means of the matrix Kronecker product, so as to obtain the sufficient conditions for the equations to have generalized columnar conjugate extension solutions as well as their generalized expressions, and then finally, the results are illustrated by numerical examples.