An Inequality of Hadamard Type for Permanents
نویسندگان
چکیده
منابع مشابه
An Inequality of Hadamard Type for Permanents
Let F be an N×N complex matrix whose jth column is the vector ~ fj in C . Let |~ fj |2 denote the sum of the absolute squares of the entries of ~ fj . Hadamard’s inequality for determinants states that | det(F )| ≤ Nj=1 |~ fj |. Here we prove a sharp upper bound on the permanent of F , which is |perm(F )| ≤ N ! NN/2 N ∏ j=1 |~ fj |, and we determine all of the cases of equality. We also discuss...
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Let A be an n-square (0, 1)-matrix, let ri denote the i-th row sum of A, i = 1 ..... n, and let per(A) denote the permanent of A. Then per(A) ~< H ri q~/-2,.1 I + V T where equality can occur if and only if there exist permutation matrices P and Q such that PAQ is a direct sum of l-square and 2-square matrices all of whose entries are 1. I f A = (ai~) is an n-square mat r ix then the permanent ...
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ژورنال
عنوان ژورنال: Methods and Applications of Analysis
سال: 2006
ISSN: 1073-2772,1945-0001
DOI: 10.4310/maa.2006.v13.n1.a1