On Orthogonal Matrices Maximizing the 1-norm

被引：12

作者：

Banica, Teodor ^{[1
]}

Collins, Benoit ^{[2
,3
]}

Schlenker, Jean-Marc ^{[4
]}

机构：

[1] Cergy Pontoise Univ, Dept Math, F-95000 Cergy Pontoise, France

[2] Univ Lyon 1, Dept Math, F-69622 Villeurbanne, France

[3] Univ Ottawa, Ottawa, ON K1N 6N5, Canada

[4] Univ Toulouse 3, Inst Math Toulouse, UMR CNRS 5219, F-31062 Toulouse 9, France

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2010年 / 59卷 / 03期

关键词：

orthogonal group; Hadamard matrix;

D O I：

10.1512/iumj.2010.59.3926

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For U is an element of O(N) we have parallel to U parallel to(1) <= N root N, with equality if and only if U = H/ root N, with H Hadamard matrix. Motivated by this remark, we discuss in this paper the algebraic and analytic aspects of the computation of the maximum of the 1-norm on O(N). The main problem is to compute the k-th moment of the 1-norm on O(N), with k -> infinity, and we discuss here the general strategy for approaching this problem, with some explicit computations at k = 1, 2 and N -> infinity.

引用

页码：839 / 856

页数：18

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