Let A be a real square matrix. A real number λ‎ is an eigenvalue of A if and only if there is a non-zero real vector x, called an eigenvector, such that Ax = λ‎x. This is equivalent to λ‎ satisfying the characteristic equation det(A − λ‎I) = 0. More generally, these definitions apply to square matrices and linear maps over other fields; in these cases the eigenvectors may be referred to as eigenfunctions, if the vector space is a function space, or as eigenstates, particularly in quantum theory.