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<p>This paper investigates solvability conditions for a constrained system of Sylvester-type quaternion tensor equations. An explicit formula of the general solution to the above system is obtained by the Moore-Penrose inverse. As an application of this system in a particular case, we establish the general solution to a system of Sylvester-type quaternion tensor equations involving <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\eta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>-Hermitian unknowns. Moreover, an algorithm with a numerical example is proposed to compute the general solution of the main system.</p>

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Solvability conditions and the general solution to a system of quaternion tensor equations with applications

  • 期刊论文

  • 发表日期：

    2026年1月5日

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  • Mahmoud Saad Mehany,
  • Qing-Wen Wang,
  • Jiale Gao

摘要

This paper investigates solvability conditions for a constrained system of Sylvester-type quaternion tensor equations. An explicit formula of the general solution to the above system is obtained by the Moore-Penrose inverse. As an application of this system in a particular case, we establish the general solution to a system of Sylvester-type quaternion tensor equations involving \(\eta \) η -Hermitian unknowns. Moreover, an algorithm with a numerical example is proposed to compute the general solution of the main system.