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arXiv · 1208.3330

Bounds on minors of binary matrices

Richard P. Brent·Judy-anne H. Osborn
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Abstract

We prove an upper bound on sums of squares of minors of {+1, -1} matrices. The bound is sharp for Hadamard matrices, a result due to de Launey and Levin (2009), but our proof is simpler. We give several corollaries relevant to minors of Hadamard matrices, and generalise a result of Turan on determinants of random {+1,-1} matrices.

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Richard P. Brent, Judy-anne H. Osborn. 2012-09-14. Bounds on minors of binary matrices. https://doi.org/10.1017/s000497271200086x

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