On orthogonal matrices maximizing the 1-norm

Teodor Banica, Benoit Collins, Jean-Marc Schlenker

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 algeb…