The Perturbations Of Some Constrained Subspaces And Their Applications

Perturbation analysis of subspaces , such as eigen-spaces , singular subspaces , and canonical subspaces, have a very wide range of applications . Rising from the least squares-total least squares (LS-TLS) problem , the constrained least squares (LSE) problem , and the constrained total least squares (CTLS) problem, we mainly discuss the problems as follows:1) Perturbations of some constrained subspaces of 1 × 2 and 2×1 block matrices , in which the rank of (1,1) block sub-matrices are unchanged , and their applications.2) Perturbations of some constrained subspaces of 2 × 2 block matrices , in which only the rank of (2,2) block sub-matrices can be changed, and perturbation analysis of the Eckart-Young-Mirsky theorem.