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Preprint
The inverse function theorem and the resolution of the Jacobian conjecture in free analysis
arXiv.org
25 Mar 2013
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.
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Details
- Title
- The inverse function theorem and the resolution of the Jacobian conjecture in free analysis
- Creators
- J. E Pascoe
- Publication Details
- arXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021880197104721