The implicit function theorem and free algebraic sets
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- by Jim Agler and John E. M$^{\mathrm {c}}$Carthy PDF
- Trans. Amer. Math. Soc. 368 (2016), 3157-3175 Request permission
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 $X$.References
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Additional Information
- Jim Agler
- Affiliation: Department of Mathematics, University of California San Diego, La Jolla, California 92093
- John E. M$^{\mathrm {c}}$Carthy
- Affiliation: Department of Mathematics, Washington University, St. Louis, Missouri 63130
- MR Author ID: 271733
- ORCID: 0000-0003-0036-7606
- Received by editor(s): February 19, 2014
- Published electronically: July 22, 2015
- Additional Notes: The first author was partially supported by National Science Foundation Grant DMS 1068830
The second author was partially supported by National Science Foundation Grant DMS 1300280 - © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 3157-3175
- MSC (2010): Primary 14M99, 16S50
- DOI: https://doi.org/10.1090/tran/6546
- MathSciNet review: 3451873