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arXiv · 1903.10386

Lipschitz property for systems of linear mappings and bilinear forms

Abdullah Alazemi·Milica Anđelić·Carlos M. da Fonseca·Vladimir V. Sergeichuk
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Abstract

Let G be a graph with undirected and directed edges. Its representation is given by assigning a vector space to each vertex, a bilinear form on the corresponding vector spaces to each directed edge, and a linear map to each directed edge. Two representations A and A' of G are called isomorphic if there is a system of linear bijections between the vector spaces corresponding to the same vertices that transforms A to A'. We prove that if two representations are isomorphic and close to each other, then their isomorphism can be chosen close to the identity.

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Abdullah Alazemi, Milica Anđelić, Carlos M. da Fonseca, Vladimir V. Sergeichuk. 2019-03-25. Lipschitz property for systems of linear mappings and bilinear forms. https://doi.org/10.1016/j.laa.2019.03.016

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