PIMS Emergent Research Seminar: Himanshu Gupta

A matrix is called totally positive if all of its minors are positive. These matrices are important in mathe- matics, but checking whether a large matrix is totally positive can be challenging. In this talk, we explore whether certain matrices associated with a totally positive matrix, such as its compounds or those obtained through Dodgson condensation, also remain totally positive. In general, we find that this is not the case. However, we provide some helpful sufficient conditions that make it easier to verify when a matrix is totally positive using these techniques. This is joint work with Shaun Fallat and Charles R. Johnson.