Equivalence of Butson-type Hadamard matrices

Patric R.J. Östergård

doi:10.1007/s10801-021-01109-8

Equivalence of Butson-type Hadamard matrices

Patric R.J. Östergård^*

^*Corresponding author for this work

Information Theory

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Abstract

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 language	English
Pages (from-to)	271-277
Number of pages	7
Journal	JOURNAL OF ALGEBRAIC COMBINATORICS
Volume	56
Issue number	2
Early online date	7 Feb 2022
DOIs	https://doi.org/10.1007/s10801-021-01109-8
Publication status	Published - Sept 2022
MoE publication type	A1 Journal article-refereed

Keywords

Butson-type Hadamard matrix
Complex matrix
Hadamard equivalence
Monomial equivalence

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Equivalence of Butson-type Hadamard matrices

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