Originally Published In
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 368, Number 5, May 2016, Pages 3157–3175 http://dx.doi.org/10.1090/tran/6546
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
Agler, Jim and McCarthy, John E., "The implicit function theorem and free algebraic sets" (2016). Mathematics Faculty Publications. 25.