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Monthly Archives: December 2012
Symmetric 01 Matrices with All Eigenvalues Positive
Recently I was surprised to learn that the only symmetric 01 matrix with all eigenvalues positive is the identity matrix. Here’s a very nice proof of this fact given in this answer of Robert Israel’s: Let A be an symmetric 01 matrix … Continue reading
Posted in linear algebra, matrices
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The Absorption Identity for Binomial Coefficients
The absorption identity for binomial coefficients is This post will give a couple of proofs of the identity and then use it to prove some other identities involving binomial coefficient sums. Proofs of the absorption identity Proof 1: Use the … Continue reading
Posted in binomial coefficients, combinatorics
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Some Uses of Duality in Linear Programming
For most of my students, the first time they see duality in linear programming their first reaction is “What’s the big deal?” There was a recent post on math.SE asking the same question. Duality in linear programming seems to me … Continue reading
Posted in linear programming
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