Journal
MATHEMATISCHE ZEITSCHRIFT
Volume 278, Issue 3-4, Pages 987-994Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00209-014-1342-2
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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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