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<p>This paper studies the core inverse of third-order quaternion tensors based on the general quaternion tensor product (gQt-product). We first derive the Hartwig–Spindelböck (H–S) decomposition for quaternion matrices and extend it to tensors via the discrete quaternion Fourier transform. Using this decomposition, we introduce the tensor core inverse, prove its existence and uniqueness, and provide an explicit representation. Furthermore, we analyze perturbations under unilateral and bilateral conditions. In both cases, we derive exact expressions for the perturbed core inverse and establish corresponding error bounds. Numerical examples validate the theoretical results.</p>

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Characteristics and perturbation analysis for the core inverse of tensors over the quaternion skew field

  • 期刊论文

  • 发表日期：

    2026年4月21日

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  • Ning Zhang,
  • Tianjuan Wu,
  • Haifeng Ma

摘要

This paper studies the core inverse of third-order quaternion tensors based on the general quaternion tensor product (gQt-product). We first derive the Hartwig–Spindelböck (H–S) decomposition for quaternion matrices and extend it to tensors via the discrete quaternion Fourier transform. Using this decomposition, we introduce the tensor core inverse, prove its existence and uniqueness, and provide an explicit representation. Furthermore, we analyze perturbations under unilateral and bilateral conditions. In both cases, we derive exact expressions for the perturbed core inverse and establish corresponding error bounds. Numerical examples validate the theoretical results.