Lipschitz property for systems of linear mappings and bilinear forms

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.

12 pages

References in corpus (4)

• Classification problems for system of forms and linear mappings
• Complexity of matrix problems
• Canonical matrices of bilinear and sesquilinear forms
• Canonical matrices of isometric operators on indefinite inner product spaces