Asymptotically optimal approximate Hadamard matrices

Boris Alexeev; John Jasper; Dustin G. Mixon

Asymptotically optimal approximate Hadamard matrices

Combinatorics 2025-11-19 v1 Functional Analysis

Authors: Boris Alexeev , John Jasper , Dustin G. Mixon

Abstract

In this paper, we study approximate Hadamard matrices, that is, well-conditioned $n\times n$ matrices with all entries in $\{\pm1\}$ . We show that the smallest-possible condition number goes to $1$ as $n\to\infty$ , and we identify some explicit infinite families of approximate Hadamard matrices.

Keywords

hadamard matrices

Cite

@article{arxiv.2511.14653,
  title  = {Asymptotically optimal approximate Hadamard matrices},
  author = {Boris Alexeev and John Jasper and Dustin G. Mixon},
  journal= {arXiv preprint arXiv:2511.14653},
  year   = {2025}
}

Comments

See the ancillary files for putatively optimal matrices and Lean code

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