This is an announcement for the paper "On orthogonal matrices maximizing the 1-norm" by Teodor Banica, Benoit Collins, and Jean-Marc Schlenker.

Abstract: For $U\in O(N)$ we have $||U||_1\leq N\sqrt{N}$, with equality if and only if $U=H/\sqrt{N}$, 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, with $k\to\infty$, and we present a number of general comments in this direction.

Archive classification: math.OA math.CO

Remarks: 17 pages

The source file(s), omx.tex: 34742 bytes, is(are) stored in gzipped form as 0901.2923.gz with size 11kb. The corresponding postcript file has gzipped size 98kb.

Submitted from: banica@picard.ups-tlse.fr

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