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We develop a method to characterize Hadamard matrices which are useful in several areas of chemistry and spectroscopy (Hadamard transform spectroscopy, stereochemistry, chemical balance, etc). We first order the Hadamard matrix according to the packed binary row labels (and column labels for skew-Hadamard matrices). The characteristic polynomial of the ordered Hadamard matrix is constructed. This technique appears to characterize and differentiate inequivalent Hadamard matrices.
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