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SOME TIDBITS ON IDEAL PROJECTORS, COMMUTING MATRICES AND THEIR APPLICATIONS

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Electronic Transactions on Numerical Analysis.

Volume 36, pp. 17-26, 2009.

Copyright2009, Kent State University.

ISSN 1068-9613.

ETNA

Kent State University http://etna.math.kent.edu

SOME TIDBITS ON IDEAL PROJECTORS, COMMUTING MATRICES AND THEIR APPLICATIONS

BORIS SHEKHTMANy

To my teacher and friend Richard Varga on the occasion of his eightieth birthday.

Abstract. The main result of this paper is the parametrization of ideal projectors onto an arbitrary finite- dimensional linear subspaceG |[x℄. This parametrization extends the previous ones by B. Mourrain and by M. Kreuzer and L. Robbiano. We also give applications of the technique developed in this paper to a question of similarity between a sequence of commuting matrices and its transpose and to the existence of real solutions to a system of polynomial equations.

Key words. Ideal projector, commuting operators, border schemes.

AMS subject classifications. Primary: 41A63, 41A10, 41A35; Secondary: 13P10.

Received March 13, 2009. Accepted for publication May 1, 2009. Published online August 24, 2009. Recom- mended by V. Mehrmann.

yDepartment of Mathematics & Statistics, University of South Florida, Tampa, FL 33620-5700, USA ([email protected]).

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