Bounds on minors of binary matrices

Richard P. Brent; Judy Anne H. Osborn

doi:10.1017/S000497271200086X

Bounds on minors of binary matrices

Richard P. Brent^*, Judy Anne H. Osborn

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

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 [' (1,-1)-matrices with near-extremal properties', SIAM J. Discrete Math. 23(2009), 1422-1440], but our proof is simpler. We give several corollaries relevant to minors of Hadamard matrices.

Original language	English
Pages (from-to)	280-285
Number of pages	6
Journal	Bulletin of the Australian Mathematical Society
Volume	88
Issue number	2
DOIs	https://doi.org/10.1017/S000497271200086X
Publication status	Published - Oct 2013

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abstract = "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 [' (1,-1)-matrices with near-extremal properties', SIAM J. Discrete Math. 23(2009), 1422-1440], but our proof is simpler. We give several corollaries relevant to minors of Hadamard matrices.",

keywords = "-1}-matrices, Cauchy-Binet formula, Hadamard matrices, binary matrices, mean square, minors, {+1",

author = "Brent, {Richard P.} and Osborn, {Judy Anne H.}",

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AU - Osborn, Judy Anne H.

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N2 - 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 [' (1,-1)-matrices with near-extremal properties', SIAM J. Discrete Math. 23(2009), 1422-1440], but our proof is simpler. We give several corollaries relevant to minors of Hadamard matrices.

AB - 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 [' (1,-1)-matrices with near-extremal properties', SIAM J. Discrete Math. 23(2009), 1422-1440], but our proof is simpler. We give several corollaries relevant to minors of Hadamard matrices.

KW - -1}-matrices

KW - Cauchy-Binet formula

KW - Hadamard matrices

KW - binary matrices

KW - mean square

KW - minors

KW - {+1

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DO - 10.1017/S000497271200086X

M3 - Article

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VL - 88

SP - 280

EP - 285

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 2

ER -

Bounds on minors of binary matrices

Abstract

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