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On varieties of commuting triples

✍ Scribed by Klemen Šivic

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
231 KB
Volume
428
Category
Article
ISSN
0024-3795

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✦ Synopsis

The problem of approximating triples of commuting n×n matrices by triples of generic matrices is equivalent to that whether the variety C(3, n) of triples of commuting matrices is irreducible. It is known that the variety is irreducible for n 7 and reducible for n 30. Using simultaneous commutative perturbations of pairs of matrices in the centralizer of the third matrix we prove that C(3, 8) is irreducible.

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