On orthogonal matrices maximizing the 1-norm

Abstract

For $U\in O(N)$ we have $||U|{|}_1\le N\sqrt{N}$, 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.

17 pages

References in corpus (2)

• Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
• On polynomial integrals over the orthogonal group

Cited by in corpus (3)

• On polynomial integrals over the orthogonal group
• The orthogonal Weingarten formula in compact form
• Real Schur norms and Hadamard matrices