2011/04/13 by Andrii Dmytryshyn, Dmytryshyn, Andrii · 1 citation
Computer Science · Engineering · Mathematics · #15A21 #15A63 #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Representation Theory (math.RT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1104.2530
openalex publication_date 2011/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For each pair of complex symmetric matrices (A,B) we provide a normal form with a minimal number of independent parameters, to which all pairs of complex symmetric matrices (\widetildeA,\widetildeB), close to (A,B) can be reduced by congruence transformation that smoothly depends on the entries of \widetildeA and \widetildeB. Such a normal form is called a miniversal deformation of (A,B) under congruence. A number of independent parameters in the miniversal deformation of a symmetric matrix pencil is equal to the codimension of the congruence orbit of this symmetric matrix pencil and is computed too. We also provide an upper bound on the distance from (A,B) to its miniversal deformation.