The eigenvector variety of a matrix pencil

Ringel CM (2017)
Linear Algebra and its Applications 531: 447-458.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Abstract / Bemerkung
Let k be a field and n, a, b natural numbers. A matrix pencil P is given by n matrices of the same size with coefficients in k, say by (b x a)-matrices, or, equivalently, by n linear transformations alpha(i) : k(a) -> k(b) with i = 1, . . . , n. We say that P is reduced provided the intersection of the kernels of the linear transformations alpha(i) is zero. If P is a reduced matrix pencil, a vector v is an element of k(a) will be called an eigenvector of P provided the subspace (alpha(1)(v),. . . , alpha(n)(v)) of k(b) generated by the elements alpha(1)(v),. . . , alpha(n)(v) is 1-dimensional. Eigenvectors are called equivalent provided they are scalar multiples of each other. The set is an element of(P) of equivalence classes of eigenvectors of P is a Zariski closed subset of the projective space P(k(a)), thus a projective variety. We call it the eigenvector variety of P. The aim of this note is to show that any projective variety arises as an eigenvector variety of some reduced matrix pencil. (C) 2017 Elsevier Inc. All rights reserved.
Stichworte
Matrix pencils; Eigenvectors; eigenvalues; Projective varieties; Kronecker modules; Quiver Grassmannians
Erscheinungsjahr
2017
Zeitschriftentitel
Linear Algebra and its Applications
Band
531
Seite(n)
447-458
ISSN
0024-3795
eISSN
1873-1856
Page URI
https://pub.uni-bielefeld.de/record/2913970

Zitieren

Ringel CM. The eigenvector variety of a matrix pencil. Linear Algebra and its Applications. 2017;531:447-458.
Ringel, C. M. (2017). The eigenvector variety of a matrix pencil. Linear Algebra and its Applications, 531, 447-458. doi:10.1016/j.laa.2017.05.004
Ringel, C. M. (2017). The eigenvector variety of a matrix pencil. Linear Algebra and its Applications 531, 447-458.
Ringel, C.M., 2017. The eigenvector variety of a matrix pencil. Linear Algebra and its Applications, 531, p 447-458.
C.M. Ringel, “The eigenvector variety of a matrix pencil”, Linear Algebra and its Applications, vol. 531, 2017, pp. 447-458.
Ringel, C.M.: The eigenvector variety of a matrix pencil. Linear Algebra and its Applications. 531, 447-458 (2017).
Ringel, Claus Michael. “The eigenvector variety of a matrix pencil”. Linear Algebra and its Applications 531 (2017): 447-458.

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Suchen in

Google Scholar