Abstract
Two matrices H_1 and H_2 with entries from a multiplicative group G are said to be monomially equivalent, denoted by H_1cong H_2, 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 H_1 cong phi (H_2) for some phi in mathrm {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.
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