Slices of matrices - a scenario for spectral theory
Ricardo S. Leite, Carlos Tomei
Abstract
Given a real, symmetric matrix S, we define the slice through S as being the connected component containing S of two orbits under conjugation: the first by the orthogonal group, and the second by the upper triangular group. We describe some classical constructions in eigenvalue computations and integrable systems which keep slices invariant -- their properties are clarified by the concept. We also parametrize the closure of a slice in terms of a convex polytope.
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