It is shown that for any two n x n complex valued matrices A, B the inequality |perA-perB|≤n||A-B||Fmax(||A||F,||B||F)^n-1 or |perA-perB|≤||A||F^n+||B||F^n holds for ||A||F =(∑i=1^n...It is shown that for any two n x n complex valued matrices A, B the inequality |perA-perB|≤n||A-B||Fmax(||A||F,||B||F)^n-1 or |perA-perB|≤||A||F^n+||B||F^n holds for ||A||F =(∑i=1^n∑j=1^n|αij|^2)^1/2 where A^H denotes the conjuagte transpose of the matrix A = (αij)n×n.展开更多
基金Supported by the Natural Science Foundation of Hubei Province(2004X157).
文摘It is shown that for any two n x n complex valued matrices A, B the inequality |perA-perB|≤n||A-B||Fmax(||A||F,||B||F)^n-1 or |perA-perB|≤||A||F^n+||B||F^n holds for ||A||F =(∑i=1^n∑j=1^n|αij|^2)^1/2 where A^H denotes the conjuagte transpose of the matrix A = (αij)n×n.