We consider Hermitian matrix valued functions depending on three parameters that vary in a bounded surface of $\R^3$ . We study how to detect when such functions have coalescing eigenvalues inside this surface. Our criterion to locate these singularities is based on a construction suggested by Stone in [20]. For generic coalescings, any such singularity is related to a particular accumulation of a certain phase, or lack thereof, as we cover the surface.

Hermitian matrices depending on three parameters: Coalescing eigenvalues.

PUGLIESE, Alessandro
2012

Abstract

We consider Hermitian matrix valued functions depending on three parameters that vary in a bounded surface of $\R^3$ . We study how to detect when such functions have coalescing eigenvalues inside this surface. Our criterion to locate these singularities is based on a construction suggested by Stone in [20]. For generic coalescings, any such singularity is related to a particular accumulation of a certain phase, or lack thereof, as we cover the surface.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/21419
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