The implicit function theorem and free algebraic sets

By Jim Agler, John E. McCarthy. 2014

54 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/2fa4fe3d56ed166c5e4d6aa1eb7fd48e1332b7ec

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In Algebra and Number Theory

1. E. Shamovich
2. Guy Salomon
3. Orr Shalit

In Applied Mathematics

1. E. Shamovich
2. Guy Salomon
3. Orr Shalit
4. Michael Hartz

In Computational Theory and Mathematics

1. E. Shamovich
2. Orr Shalit
3. Guy Salomon

Citations in the corpus

• Algebras of bounded noncommutative analytic functions on subvarieties of the noncommutative unit ball (2017, background): “Recently, many works laid out the foundations of noncommutative free analysis, such as [44], [3,4,6] and [67].”