Almost Hadamard matrices: general theory and examples

Details Almost Hadamard matrices: general theory and examples Almost Hadamard matrices: general theory and examples

2012-02-09

arxiv.org/abs/1202.2025v1

Mathematics

Combinatorics

24 pages

Scientific paper

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.

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