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<p>In this paper, we introduce a novel approach for analyzing and solving a system of Sylvester-type quaternion matrix equations. We first establish the equivalence canonical form of a set of 2<i>n</i> quaternion matrices by using the Quotient Singular Value Decomposition (QSVD) for multiple matrices. With this canonical form as a foundation, some practical solvability conditions of a general system of coupled Sylvester-type quaternion matrix equations are derived. Compared to the Moore-Penrose inverse method found in the literature, our approach is simpler and more fundamental. Finally, we apply this system and its equivalence form to simultaneous encryption and decryption of color images with the corresponding PSNR values SSIM values demonstrating the effectiveness of our approach.</p>

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Qsvd method for arbitrary multiple sylvester-type coupled quaternion matrix equations with applications

  • 期刊论文

  • 发表日期：

    2025年12月18日

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  • Zhuo-Heng He,
  • Li-Wei Ye,
  • Yun-Ze Xu,
  • Mei-Ling Deng

摘要

In this paper, we introduce a novel approach for analyzing and solving a system of Sylvester-type quaternion matrix equations. We first establish the equivalence canonical form of a set of 2n quaternion matrices by using the Quotient Singular Value Decomposition (QSVD) for multiple matrices. With this canonical form as a foundation, some practical solvability conditions of a general system of coupled Sylvester-type quaternion matrix equations are derived. Compared to the Moore-Penrose inverse method found in the literature, our approach is simpler and more fundamental. Finally, we apply this system and its equivalence form to simultaneous encryption and decryption of color images with the corresponding PSNR values SSIM values demonstrating the effectiveness of our approach.