The inverse function theorem and the resolution of the Jacobian conjecture in free analysis
Functional Analysis
2014-07-01 v1 Commutative Algebra
Algebraic Geometry
Complex Variables
Abstract
We establish an invertibility criterion for free polynomials and free functions evaluated on some tuples of matrices. We show that if the derivative is nonsingular on some domain closed with respect to direct sums and similarity, the function must be invertible. Thus, as a corollary, we establish the Jacobian conjecture in this context. Furthermore, our result holds for commutative polynomials evaluated on tuples of commuting matrices.
Keywords
Cite
@article{arxiv.1303.6011,
title = {The inverse function theorem and the resolution of the Jacobian conjecture in free analysis},
author = {J. E. Pascoe},
journal= {arXiv preprint arXiv:1303.6011},
year = {2014}
}