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arXiv · 2603.16539

Perturbation Analysis of the QT-Drazin Inverse of Quaternion Tensors via the QT-Product

Yue Zhao·Daochang Zhang·Jingqian Li·Dijana Mosic
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Abstract

The motivation of this paper is to investigate the perturbation theory for the QT-Drazin inverse of quaternion tensors under the QT-product via the associated $z$-block circulant representation. A fundamental relationship between the QT-Drazin inverse of $\mathtt{bcirc}_z(\mathcal A)$ and the $z$-block circulant form of $\mathcal A^D$ is established. Moreover, the QT-index of a quaternion tensor is characterized by the indices of the diagonal blocks in the corresponding block-diagonalized matrix. As a consequence, a representation of the QT-Drazin inverse in terms of the QT-Moore--Penrose inverse is derived, which offers a practical approach for its direct computation in MATLAB. Furthermore, a decomposition theory for the QT-Drazin inverse is developed by combining the structure of $z$-block circulant matrices with the Jordan decomposition of quaternion matrices. Numerical examples are provided to demonstrate the theoretical results and computational feasibility.

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Yue Zhao, Daochang Zhang, Jingqian Li, Dijana Mosic. 2026-03-17. Perturbation Analysis of the QT-Drazin Inverse of Quaternion Tensors via the QT-Product. https://arxiv.org/abs/2603.16539

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