Monthly Archives: December 2012

Symmetric 0-1 Matrices with All Eigenvalues Positive

Recently I was surprised to learn that the only symmetric 0-1 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 0-1 matrix … Continue reading

Posted in linear algebra, matrices | Leave a comment

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 | 3 Comments

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 | 1 Comment