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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Matrices with eigenvectors in a given subspace


Authors: Giorgio Ottaviani and Bernd Sturmfels
Journal: Proc. Amer. Math. Soc. 141 (2013), 1219-1232
MSC (2010): Primary 15A18; Secondary 13P25, 14N15, 93B25
Published electronically: August 31, 2012
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Abstract: The Kalman variety of a linear subspace in a vector space consists of all endomorphisms that possess an eigenvector in that subspace. We study the defining polynomials and basic geometric invariants of the Kalman variety.


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Additional Information

Giorgio Ottaviani
Affiliation: Department of Mathematics, University of Florence, viale Morgagni 67/A, 50134 Florence, Italy
Email: ottavian@math.unifi.it

Bernd Sturmfels
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Email: bernd@math.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11404-2
PII: S 0002-9939(2012)11404-2
Keywords: Eigenvectors, Kalman’s observability condition, determinantal varieties, Gröbner bases, Hilbert series, vector bundles, Chern classes, resolution of singularities
Received by editor(s): December 7, 2010
Received by editor(s) in revised form: May 23, 2011, and August 19, 2011
Published electronically: August 31, 2012
Communicated by: Harm Derksen
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.