Properties of the Approximations of a Matrix which Lower its Rank
Krystyna Ziętak · IMA Journal of Numerical Analysis · 1989
Let C be a real m × n matrix. This paper considers the general properties of the best approximations E to C in an arbitrary norm by matrices of rank ≦r. The case in which rank C = n, r = n − 1, and ‖·‖ is a separable norm is dealt with separately. For this particular case, the form of every best approximation E and an estimate of the error ‖C − E‖ are given. The paper also investigates when, for this particular case, the best approximation E is unique.