Almost Hadamard matrices: general theory and examples

Abstract

We develop a general theory of "almost Hadamard matrices". These are by definition the matrices $H\in M_N(\mathbb{R})$ having the property that $U=H/\sqrt{N}$ is orthogonal, and is a local maximum of the 1-norm on O(N). Our study includes a detailed discussion of the circulant case ($H_{ij}={\gamma }_{j-i}$) and of the two-entry case ($H_{ij}\in x,y$), with the construction of several families of examples, and some 1-norm computations.

24 pages

References in corpus (3)

• Real Mutually Unbiased Bases
• On polynomial integrals over the orthogonal group
• Real and complex unbiased Hadamard matrices