二元张量积的Ky Fan控制
Ky Fan majorization for binary tensor products
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中文总结 AI 辅助
该研究对矩阵二元张量积之和的奇异值的Ky Fan型控制关系给出简短证明，推广了Alhejji的结果，并将其应用于完全正映射与其Kraus算子奇异值的控制关系研究。
中文摘要 AI 辅助
我们对矩阵的二元张量积之和的奇异值的Ky Fan型控制关系给出了一个简短证明，这将Alhejji的结果（arXiv:2410.18254）从两个求和项推广到任意求和项，且从正矩阵推广到任意矩阵；作为应用，我们证明了完全正映射的奇异值与其Kraus算子的奇异值之间存在控制关系。
英文摘要
We provide a short proof of a Ky Fan-type majorization relation for the singular values of a sum of binary tensor products of matrices. This generalizes Alhejji's result (arXiv:2410.18254) from two summands to arbitrary sums and from positive matrices to arbitrary matrices. As an application, we show a majorization relation between the singular values of a completely positive map and those of its Kraus operators.
