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Sylvester Hadamard matrices revisited
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Abstract
In this work we revisited some properties of Sylvester Hadamard matrices of order 2k. Based onlyon the existence of a base from which any Sylvester Hadamard matrix can be constructed, we prove that theirrows (columns) are closed under addition and that the numbers of sign interchanges along any row (column)give all integers 0, 1, . . . , 2k − 1 in some order. These two properties can be used to check if an Hadamardmatrix is equivalent to a Sylvester Hadamard matrix.
Title: Sylvester Hadamard matrices revisited
Description:
Abstract
In this work we revisited some properties of Sylvester Hadamard matrices of order 2k.
Based onlyon the existence of a base from which any Sylvester Hadamard matrix can be constructed, we prove that theirrows (columns) are closed under addition and that the numbers of sign interchanges along any row (column)give all integers 0, 1, .
.
.
, 2k − 1 in some order.
These two properties can be used to check if an Hadamardmatrix is equivalent to a Sylvester Hadamard matrix.
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