Recently, Bradley and Mangasarian studied the problem of finding the neares
t plane to m given points in R-n in the least square sense. They showed tha
t the problem reduces to finding the least eigenvalue and associated eigenv
ector of a certain n x n symmetric positive-semidefinite matrix. We extend
this result to the general problem of finding the nearest q-flat to m point
s, with 0 less than or equal to q less than or equal to n - 1.