Minimization of the Frobenius norm of a complex matrix using planar similarities Original Research Article

We investigate one step of an optimal norm-reducing method with shear Tkj on the pivot pair View the MathML source without the usual restriction det(Tkj)=1 [Eberlein, SIAM J. Appl. Math. 10 (1962) 74–88; Paardekooper, Doctoral Dissertation, Eindhoven Institute of Technology, 1969]. The norm View the MathML source can be expressed in terms of the nontrivial elements of X=Z∗Z. Here Z is the essential part of the shear Tkj. The resolvent and structural parameters that appear by solving the problem View the MathML source are invariant with respect to some unitary shear transformations. This study provides invariant formulas for Paardekooperʹs method that is based on the solution of the problem View the MathML source.