Closest normal matrix finally found!

A method of finding the closest normal matrix in the Frobenius matrix norm is developed. It is shown that if a matrix is represented in those coordinates where its closest normal matrix is diagonal, its restriction to any pair of coordinate directions is a multiple of a real diagonal and skew nondiagonal 2×2 matrix. A convergent algorithm to bring an arbitrary matrix into that form is described and results of numerical tests are reported.Dedicated to the memory of Peter Henrici (1923–1987).