Аннотация
Let X0 be a square matrix (complex or otherwise) and u0 a (normalized) eigenvector associated with an eigenvalue λ 0 of X0, so that the triple (X0,u0,λ 0) satisfies the equations Xu = λu, u0 * u=1. We investigate the conditions under which unique differentiable functions λ(X) and u(X) exist in a neighborhood of X0 satisfying λ (X0)=λ 0,u(X0)=Xu=λ u, and u0 * u=1. We obtain the first and second derivatives of λ(X) and the first derivative of u(X). Two alternative expressions for the first derivative of λ(X) are also presented.
Пользователи данного ресурса
Пожалуйста,
войдите в систему, чтобы принять участие в дискуссии (добавить собственные рецензию, или комментарий)