Hello everybody! For my 10 minute talk next week I will be discussing the properties and significance of Hankel and Hilbert Matrices. These are famous symmetric matrices that have certain characteristics that cause them to be problematic. Hankel matrices consist of a square matrix where the entry for each skew-diagonal element from left to right in the matrix is constant. The Hilbert matrix is a specific type of Hankel matrix where each entry for the skew-diagonals is also an ascending unit fraction. The properties for both these types of matrices causes them to be ill-conditioned, which means that a small change to any constant coefficient entry creates a large change in the solution to the matrix. This being so, you have to be extra careful when solving Hilbert and Hankel matrices. Hilbert matrices are also nearly singular, which means the determinant is always very close to zero. When the determinant of a matrix is zero it means that the matrix does not have an inverse, so when computing the inverse of Hilbert matrices you may run into several problems/computational errors.
