Critical points of matrix least squares distance functions Original Research Article

A classical problem in matrix analysis and total least squares estimation is that of finding a best approximant of a given matrix by lower rank ones. In this paper the critical points and the local minimum of the distance function fA(X) = short parallelA − Xshort parallel2 on varieties of fixed rank symmetric, skew-symmetric, and rectangular matrices X are determined. Our results extend earlier ones of Eckart and Young and of Higham.