On perturbations of some constrained subspaces

Perturbation bounds of subspaces, such as eigen-spaces, singular subspaces, and canonical subspaces, have been extensively studied in the literature. In this paper, we study perturbations of some constrained subspaces of 1×2, 2×1, and 2×2 block matrices, in which only one of the sub-matrices can be changed. Such problems rise from the least squares–total least squares problem, the constrained least squares problem, and the constrained total least squares problem.