The Eckart-Young-Mirsky theorem solves the problem of approximating a matrix by one of lower rank. However, the approximation generally differs from the original in all its elements. In this paper it is shown how to obtain a best approximation of lower rank in which a specified set of columns of the matrix remains fixed. The paper concludes with some applications of the generalization. © 1987.
Golub, G. H., Hoffman, A., & Stewart, G. W. (1987). A generalization of the Eckart-Young-Mirsky matrix approximation theorem. Linear Algebra and Its Applications, 88–89(C), 317–327. https://doi.org/10.1016/0024-3795(87)90114-5