A sign test for detecting the equivalence of Sylvester Hadamard matrices |
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Authors: | Marilena Mitrouli |
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Institution: | 1.Department of Mathematics,University of Athens,Athens,Greece |
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Abstract: | In this paper we show that every matrix in the class of Sylvester Hadamard matrices of order 2
k
under H-equivalence can have full row and column sign spectrum, meaning that tabulating the numbers of sign interchanges
along any row (or column) gives all integers 0,1,...,2
k
− 1 in some order. The construction and properties of Yates Hadamard matrices are presented and is established their equivalence
with the Sylvester Hadamard matrices of the same order. Finally, is proved that every normalized Hadamard matrix has full
column or row sign spectrum if and only if is H-equivalent to a Sylvester Hadamard matrix. This provides us with an efficient
criterion identifying the equivalence of Sylvester Hadamard matrices. |
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Keywords: | |
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