Eigenstates, eigenvectors, and eigenvalues

The eigenstates of  a system are its characteristic states, the eigenvectors are the characteristic vectors describing the states,  and the eigenvalues are the characteristic values representing the states of the system. For example, if we consider a one dimensional quantum harmonic oscillator, its ground state is one of its eigenstates which is represented by the eigenvector |g> and the eigenvalue is (one-half *hbar*omega), where (omega) is the frequency of the oscillator. The other eigenstates of the oscillator are the excited states |e> with the increase of energy by (hbar*omega) while climbing up from the ground state.