Equivalence of Butson-type Hadamard matrices

Patric R.J. Östergård*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Two matrices H1 and H2 with entries from a multiplicative group G are said to be monomially equivalent, denoted by H1≅ H2, if one of the matrices can be obtained from the other via a sequence of row and column permutations and, respectively, left- and right-multiplication of rows and columns with elements from G. One may further define matrices to be Hadamard equivalent if H1≅ ϕ(H2) for some ϕ∈ Aut (G). For many classes of Hadamard and related matrices, it is straightforward to show that these are closed under Hadamard equivalence. It is here shown that also the set of Butson-type Hadamard matrices is closed under Hadamard equivalence.

Original languageEnglish
Pages (from-to)271-277
Number of pages7
Issue number2
Early online date7 Feb 2022
Publication statusPublished - Sept 2022
MoE publication typeA1 Journal article-refereed


  • Butson-type Hadamard matrix
  • Complex matrix
  • Hadamard equivalence
  • Monomial equivalence


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