Singular milnor numbers of non-isolated matrix singularities

In this dissertation we obtain formulas to describe the local topology of certain non-isolated matrix singularities. We find free divisors in various vector spaces of matrices which include the hypersurface of singular matrices as a component, and use these to express the singular Milnor numbers of matrix singularities in terms of the codimensions of groups of equivalences. On the spaces of symmetric and all n x n matrices, these free divisors arise through representations of finite dimensional solvable Lie groups; on the space of skew-symmetric matrices, we extend a finite-dimensional representation of a solvable Lie algebra to an infinite-dimensional one.