Ranks of Hadamard Matrices and Equivalence of Sylvester—Hadamard and Pseudo-Noise Matrices
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In this paper we obtain several results on the rank properties of Hadamard matrices (including Sylvester-Hadamard matrices) as well as generalized Hadamard matrices. These results are used to show that the classes of (generalized) Sylvester-Hadamard matrices and of (generalized) pseudo-noise matrices are equivalent, i.e., they can be obtained from each other by means of row/column permutations.