Let be a real eigenvalue of the real n n matrix A, and v1, ..., vk a basis for the associated eigenspace V

Let λ be a real eigenvalue of the real n × n matrix A, and v1, ..., vk a basis for the associated eigenspace Vλ Suppose w ∈ Cn is a complex eigenvector, so Aw = λw. Prove that w = c1 v1 + ... + ckvk is a complex linear combination of the real eigenspace basis.