The inverse function theorem and the Jacobian conjecture for free analysis

By James Eldred Pascoe. 2013

51 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b7e7919ffd8da0e39554a55fc82d3ec082dc9fb6

Citations in the corpus

• The implicit function theorem and free algebraic sets (2014, unknown): “Theorem 1.5.”