Ky Fan majorization for binary tensor products
Michael M. Wolf, Yuanheng Zhou
Abstract
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.
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