Submatrices of Hadamard matrices: complementation results

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Teo Banica
Ion Nechita
Jean-Marc Schlenker


Two submatrices A, D of a Hadamard matrix H are called complementary if, up to a permutation of rows and columns, H =  . In this paper, an explicit formula for the polar decomposition of D is found. As an application, it is shown that under suitable smallness assumptions on the size of A, the complementary matrix D is an almost Hadamard sign pattern, i.e., its rescaled polar part is an almost Hadamard matrix.

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