Ky Fan majorization for binary tensor products
arXiv:2607.27116
summary
The paper proves a Ky Fan‑type majorization inequality for the singular values of sums of binary tensor products of matrices, extending previous results to any number of summands and to arbitrary matrices, and applies it to relate singular values of completely positive maps to those of their Kraus operators.
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.
pi pages
Topics & keywords
#majorization#singular values#tensor products#matrix analysis#completely positive mapsKy Fan inequalitybinary tensor productKraus operatorssingular value majorization