Geodesic
Some tidbits on ideal projectors, commuting matrices and their applications
Electronic transactions on numerical analysis, Tome 36 (2010)
The main result of this paper is the parametrization of ideal projectors onto an arbitrary finitedimensional linear subspace G $\subset $k[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.
Classification : 41A63, 41A10, 41A35, 13P10
Keywords: ideal projector, commuting operators, border schemes 
@article{ETNA_2010__36__a10,
     author = {Shekhtman,  Boris},
     title = {Some tidbits on ideal projectors, commuting matrices and their applications},
     journal = {Electronic transactions on numerical analysis},
     year = {2010},
     volume = {36},
     zbl = {1189.13023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2010__36__a10/}
}
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%J Electronic transactions on numerical analysis
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Shekhtman,  Boris. Some tidbits on ideal projectors, commuting matrices and their applications. Electronic transactions on numerical analysis, Tome 36 (2010). http://geodesic.mathdoc.fr/item/ETNA_2010__36__a10/