Stability of self-adjoint square roots and polar decompositions in indefinite scalar product spaces

AbstractContinuity properties of factors in polar decompositions of matrices with respect to indefinite scalar products are studied. The matrix having the polar decomposition and the indefinite scalar product are allowed to vary. Closely related properties of a self-adjoint (with respect to an indefinite scalar product) perturbed matrix to have a self-adjoint square root, or to have a representation of the form X*X, are also studied