On the number of crossings in the spectrum of a hermitian matrix which depends on a real parameter

T.P. Valkering

doi:10.1016/0031-8914(71)90107-8

On the number of crossings in the spectrum of a hermitian matrix which depends on a real parameter

T.P. Valkering

Computational Materials Science

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Abstract

Intersection of the eigenvalues ε_i(h) of an n-dimensional hermitian matrix A + hB (h being a real parameter) is discussed. An upper limit for the number of intersections is derived in terms of the rank of the Gramian of the symmetrized products of order 0, 1, …, n — 1 of A and B.

Original language	English
Pages (from-to)	117-124
Journal	Physica
Volume	53
Issue number	1
DOIs	https://doi.org/10.1016/0031-8914(71)90107-8
Publication status	Published - 1971

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10.1016/0031-8914(71)90107-8

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Cite this

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title = "On the number of crossings in the spectrum of a hermitian matrix which depends on a real parameter",

abstract = "Intersection of the eigenvalues εi(h) of an n-dimensional hermitian matrix A + hB (h being a real parameter) is discussed. An upper limit for the number of intersections is derived in terms of the rank of the Gramian of the symmetrized products of order 0, 1, …, n — 1 of A and B.",

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AB - Intersection of the eigenvalues εi(h) of an n-dimensional hermitian matrix A + hB (h being a real parameter) is discussed. An upper limit for the number of intersections is derived in terms of the rank of the Gramian of the symmetrized products of order 0, 1, …, n — 1 of A and B.

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DO - 10.1016/0031-8914(71)90107-8

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VL - 53

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JF - Physica

SN - 0031-8914

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