The topology of isospectral manifolds of tridiagonal matrices (Q762807)
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scientific article; zbMATH DE number 3890370
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The topology of isospectral manifolds of tridiagonal matrices |
scientific article; zbMATH DE number 3890370 |
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The topology of isospectral manifolds of tridiagonal matrices (English)
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1984
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Let M be the set of real, symmetric, tridiagonal \(n\times n\) matrices with fixed spectrum without multiple eigenvalues. This paper deals with the description of the topological properties of M. It is shown that M is a compact orientable smooth manifold with universal covering space homeomorphic to \({\mathbb{R}}^{n-1}\). The Euler characteristic is calculated. A regular CW-decomposition of M is obtained. The Toda vector field on M is used as an important technical tool.
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tridiagonal matrices with fixed spectrum
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universal covering space
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Euler characteristic
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CW-decomposition
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Toda vector field
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