Volume 36, pp. 17-26, 2009-2010.

Some tidbits on ideal projectors, commuting matrices and their applications

Boris Shekhtman

Abstract

The main result of this paper is the parametrization of ideal projectors onto an arbitrary finite-dimensional linear subspace $G\subset \mathbf{k}[\mathbf{x}]$. 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.

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Key words

Ideal projector, commuting operators, border schemes.

AMS subject classifications

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