Structural stability of quadruples of matrices (Q1923153)

The authors study the perturbations of quadruples of matrices by means of their orthogonal miniversal deformation. In particular they obtain a characterization of the structural stability of quadruples of matrices, in terms of its numerical invariants. The main results are Theorem A, which describes the orthogonal miniversal deformation of quadruple of matrices, and Theorem B, which gives the desired characterization of the structurally stable quadruples of matrices. In Section I, the authors recall the natural equivalence relation between quadruples of matrices. The authors prove that the equivalence classes are regular submanifolds and obtain a description of their tangent spaces. Section II contains the proof of Theorem A and Section III is devoted to Theorem B.