Abstract
We present a preliminary study of Schur norms ‖ M ‖ S = max { ‖ M ∘ C ‖ : ‖ C ‖ = 1 } , where M is a matrix whose entries are ± 1 , and ∘ denotes the entrywise (i.e. Schur or Hadamard) product of the matrices. We recover a result of Johnsen that says that, if such a matrix M is n × n , then its Schur norm is bounded by n , and equality holds if and only if it is a Hadamard matrix. We develop a numerically efficient method of computing Schur norms, and as an application of our results we present several almost Hadamard matrices that are better than were previously known.
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