(untitled) (Journal of Computational Mathematics, 2018)
Let A be an n× n nonsingular real matrix, which has singular value decomposition A=UV^T. Assume A is perturbed to A and A has singular value decomposition A=UV^T. It is proved that \|UV^T-UV^T\|_F≤ 2σ_n\|A-A\|_F, where σ_n is the minimum singular value of A; \|\|_F denotes the Frobenius norm and n is the dimension of A. This inequality is applicable to the computational error estimation of orthogonalization of a matrix, especially in the strapdown inertial navigation system.