Counting Lower Hessenberg Matrices

Meeting Time: Sept. 15, 2009, 2:00-2:50pm

Abstract: Oftentimes it is interesting to study sets of matrices that have a certain zero pattern. In linear algebra, knowing that a matrix is triangular or diagonal is extremely helpful in computing the determinant or determining eigenvalues, as well as determining whether certain other properties, such as singularity, hold. In combinatorics, we may take a very different approach by counting the number of matrices that follow a specific zero pattern under various restrictions. In my talk, I will present some work I did as an undergraduate studying matrices with the Hessenberg zero pattern and unraveling the beautiful structure these matrices exhibit.