Let A be a square matrix with real entries, and let λ be its complex eigenvalue. Suppose v = (v1, v2, . . . , vn) T is a corresponding eigenvector, Av = λv. Prove that the λ is an eigenvalue of A and Av = λv. Here v is the complex conjugate of the vector v, v := (v1, v2, . . . , vn) T .