Abstract
In this paper, we work for the inverse quadratic eigenvalue problem of constructing real and symmetric matrices C and K such that Q(λ)=λ2I+λC+K has n prescribed eigenvalues with corresponding eigenvectors which are linearly independent and n prescribed eigenvalues without corresponding eigenvectors.Next, we concert about that if the number of prescribed eigenpairs is less than n, then we convert the eigenpair into a new eigenpair by QR decomposition and lower the size of matrix.