Spectral properties of sums of Hermitian matrices and algebraic geometry

Abstract : It is shown that all the eigenvectors of a sum of Hermitian matrices belong to the same algebraic variety. A polynomial system characterizing this variety is given and a set of nonlinear equations is derived which allows the construction of the variety. Moreover, in some specific cases, explicit expressions for the eigenvectors and eigenvalues can be obtained. Explicit solutions of selected models are also derived.
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Submitted on : Wednesday, March 2, 2016 - 11:06:11 AM
Last modification on : Monday, October 15, 2018 - 3:46:02 PM

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P. Chau Huu-Tai, P. van Isacker. Spectral properties of sums of Hermitian matrices and algebraic geometry. Journal of Physics A: Mathematical and General , IOP Publishing, 2016, 49 (15), pp.155301. ⟨10.1088/1751-8113/49/15/155301⟩. ⟨in2p3-01281429⟩

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