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arXiv · 0901.2923

On orthogonal matrices maximizing the 1-norm

Teodor Banica·Benoit Collins·Jean-Marc Schlenker
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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.

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Teodor Banica, Benoit Collins, Jean-Marc Schlenker. 2009-01-19. On orthogonal matrices maximizing the 1-norm. https://doi.org/10.1512/iumj.2010.59.3926

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