Journal
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 368, Issue 5, Pages 3157-3175Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/tran/6546
Keywords
NC functions; free holomorphic functions; free algebraic sets
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Funding
- National Science Foundation [DMS 1068830, DMS 1300280]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1361720] Funding Source: National Science Foundation
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We prove an implicit function theorem for non-commutative functions. We use this to show that if p(X, Y) is a generic non-commuting polynomial in two variables and X is a generic matrix, then all solutions Y of p(X, Y) = 0 will commute with X.
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