On orthogonal matrices maximizing the 1-norm Teodor BanicaBenoit CollinsJean-Marc Schlenker 47A3005B20orthogonal groupHadamard matrix 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 on $O(N)$, with $k \to \infty$, and we discuss here the general strategy for approaching this problem, with some explicit computations at $k = 1$, $2$ and $N \to \infty$. Indiana University Mathematics Journal 2010 text pdf 10.1512/iumj.2010.59.3926 10.1512/iumj.2010.59.3926 en Indiana Univ. Math. J. 59 (2010) 839 - 856 state-of-the-art mathematics http://iumj.org/access/