Minimizing the Euclidean norm of a complex matrix by plane similarities (Q676031)

The author discusses an algebraic solution of the problem to minimize the Frobenius norm of a complex \(n\times n\)-matrix under plane \((k,l)\)-similarities, i.e. similarities that act only on the \(k\)-th and \(l\)-th row and the \(k\)-th and \(l\)-th column of the matrix \((k\neq l)\). The problem is transferred into a canonical form. The two cases of an ``inner minimum'' and of a proper infimum are discussed separately. By an elimination process two polynomials of degree three and five (resolvents) arise whose coefficients (structure parameters) are discussed thoroughly. Some numerical examples are given.