Hollow symmetric nonnegative matrices

**Speaker:**Professor Charles Johnson (College of William and Mary, Virginia)

**Time:** 4.00PM

**Date:** Monday December 10th 2012

**Location:** Casl Seminar Room (Belfield Office Park)

**Abstract:**

An n-by-n matrix is hollow if its diagonal is all 0. We consider not only the possible eigenvalues of hollow, symmetric, nonnegative (HSN) matrices, but the special structure of HSN matrices with few negative eigenvalues. In the special case of adjacency matrices of graphs, the number of negative eigenvalues necessarily grows with n (the number of vertices or the size of the matrices). This remains true under a variety of assumptions about the distribution of off-diagonal entries. Nonetheless, we show that for each n, the number of possible negative eigenvalues is an HSN matrix can be any number form 2 to n-1. The HSN matrices exhibiting small numbers have remarkable structure among their Schur complements. There is an interesting link with copositive matrices.

**Series:** ** Algebra Seminar Series**

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