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arXiv · 1311.0764

Submatrices of Hadamard matrices: complementation results

Teo Banica·Ion Nechita·Jean-Marc Schlenker
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Abstract

Two submatrices $A,D$ of a Hadamard matrix $H$ are called complementary if, up to a permutation of rows and columns, $H=[^A_C{\ }^B_D]$. We find here an explicit formula for the polar decomposition of $D$. As an application, we show 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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Teo Banica, Ion Nechita, Jean-Marc Schlenker. 2013-11-04. Submatrices of Hadamard matrices: complementation results. https://arxiv.org/abs/1311.0764

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