关于对偶复矩阵的笛卡尔分解的酉不变范数不等式
Unitary Invariant Norm Inequalities for Cartesian Decompositions of Dual Complex Matrices
摘要: 研究了对偶复矩阵的笛卡尔分解的酉不变范数不等式。给出了对偶复矩阵的笛卡尔分解的定义。利用对偶向量间的优超关系以及对偶复矩阵的Mirsky定理证明了对偶复矩阵的笛卡尔分解的一个酉不变范数不等式。该不等式揭示了一个对偶复矩阵与其笛卡尔分解中两个对偶Hermite复矩阵的特征值的酉不变范数的数量关系。
Abstract: Unitarily norm inequalities for the Cartesian decomposition of dual complex matrices are studied. The definition of Cartesian decomposition of a dual complex matrix is defined. By using the majorization relation between dual vectors and Mirsky theorem of dual complex matrices, a unitarily norm inequality for the Cartesian decomposition of dual complex matrices is proved, which reveals the quantity relation between the unitarily norm of a dual complex matrix and the two dual Hermitian complex matrices in its Cartesian decomposition.
文章引用：刘霞. 关于对偶复矩阵的笛卡尔分解的酉不变范数不等式[J]. 理论数学, 2026, 16(2): 154-165. https://doi.org/10.12677/pm.2026.162044

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