Rellich's perturbation theorem on Hermitian matrices of holomorphic functions (Q1084467)
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scientific article; zbMATH DE number 3979263
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Rellich's perturbation theorem on Hermitian matrices of holomorphic functions |
scientific article; zbMATH DE number 3979263 |
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Rellich's perturbation theorem on Hermitian matrices of holomorphic functions (English)
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1986
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A finite dimensional linear operator which is symmetric and depends analytically on a real parameter \(\epsilon\) has an orthonormal basis of eigenvectors depending also analytically on \(\epsilon\). A short proof of this theorem of Rellich is given. It is based on the fact that the ring of functions which are holomorphic in a region of the complex plane is an elementary divisor domain.
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principal axis theorem
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orthonormal basis of eigenvectors
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theorem of Rellich
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elementary divisor domain
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