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<正>It is shown that for any two n×n complex valued matrices A, B the inequality |perA-perB|≤n‖A-B‖Fmax(‖A‖F,‖B‖F)n-1 or |perA-perB|≤‖A‖Fn+‖B‖Fn holds for where AH denotes the conjuagte transpose of the matrix A=(aij)n×n.