Generalized Eulerian numbers and the topology of the Hessenberg variety of a matrix (Q1113614)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Generalized Eulerian numbers and the topology of the Hessenberg variety of a matrix |
scientific article; zbMATH DE number 4080764
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generalized Eulerian numbers and the topology of the Hessenberg variety of a matrix |
scientific article; zbMATH DE number 4080764 |
Statements
Generalized Eulerian numbers and the topology of the Hessenberg variety of a matrix (English)
0 references
1988
0 references
It is shown that the Hessenberg variety of degree p for a matrix A is smooth and connected if A has distinct eigenvalues, and its Betti numbers are characterized. In the case when the eigenvalues of A have distinct moduli, these results are applied to determine the dimension and topology of the submanifold of U(n) consisting of those unitary matrices P for which \(A_ 0=P^{-1}AP\) is in Hessenberg form and for which the diagonal entries of the QR-iteration initialized at \(A_ 0\) converge to a given permutation of the eigenvalues.
0 references
Eulerian numbers
0 references
Hessenberg variety
0 references
Betti numbers
0 references
eigenvalues
0 references
Hessenberg form
0 references
QR-iteration
0 references
0 references
