The implicit function theorem and free algebraic sets

Authors

Jim Agler
John E. McCarthy, Washington University in St LouisFollow

Author's School

Arts & Sciences

Author's Department

Mathematics

Document Type

Article

Publication Date

5-2016

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

Abstract

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

Comments

Preprint version of article 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 © Copyright 2015 American Mathematical Society

ORCID

http://orcid.org/0000-0003-0036-7606

Recommended Citation

Agler, Jim and McCarthy, John E., "The implicit function theorem and free algebraic sets" (2016). Mathematics Faculty Publications. 25.
https://openscholarship.wustl.edu/math_facpubs/25