Abstract: Copositivity is a generalization of positive semidefiniteness. It has applications in economics, operations research, and statistics. An $n$-by-$n$ real matrix $A$ is copositive (CoP) if $x^TAx \ge 0$ for any nonnegative vector $x \ge 0$. The CoP matrices form a proper cone. A CoP matrix is ordinary if it can be written as the sum of a positive semidefinite (PSD) matrix and a symmetric nonnegative (sN) matrix. When $n < 5$, all copositive matrices are ordinary. However, recognition that a given CoP matrix is ordinary and the determination of an ordinary decomposition is an unresolved issue. Here, we make observations about CoP-preserving operations, make progress about the recognition problem, and discuss the relationship between the recognition problem and the PSD completion problem. We also mention the problem of copositive spectra and its relation to the symmetric nonnegative inverse eigenvalue problem.
|10/06||Gabriel Martins (Sacramento State)||Title TBA|
|9/29||Cordelia Li'22||Copositive matrices, their dual, and the Recognition Problem|
|9/22||Merielyn Sher'22||Enumerating minimum path covers of trees|
|9/15||Bjoern Muetzel (Eckerd College)||Harmonic forms on pinched surfaces (Slides)|
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