Asymptotically optimal approximate Hadamard matrices

by Boris Alexeev, John Jasper, and Dustin G. Mixon

Abstract

In this paper, we study approximate Hadamard matrices, that is, well-conditioned \(n\times n\) matrices with all entries in \(\{\pm 1\}\). 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.

Approximate citation

Boris Alexeev, John Jasper, and Dustin G. Mixon
Asymptotically optimal approximate Hadamard matrices

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