Computing matrix symmetrizers, finally possible via the Huang and Nong algorithm.

By a theorem of Frobenius (F.G. Frobenius,Über die mit einer Matrix vertauschbaren Matrizen, Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin (1910), pp. 3–15 (also in Gesammelte Abhandlungen, Band 3, Springer 1968. pp. 415–427)), every matrixAn,nover any field 𝔽 is the product of two symmetric ones. Using the algorithm of Huang and Nong (J. Huang and L. Nong,An iterative algorithm for solving finite-dimensional linear operator equations T(x) = f with applications, Linear Algebra Appl. 432 (2010), pp. 1176–1188) for linear systems, we develop an algorithm to compute a symmetric matrixS = ST ∈ 𝔽n,nfor whichSAis symmetric for any given square matrixA ∈ 𝔽n,nwhere 𝔽 = ℝ or ℂ. The algorithm is implemented and tested in MATLAB. [ABSTRACT FROM AUTHOR]