In mathematical analysis , one of a set of discrete values of a parameter, k , in an equation of the form L x = k x .
Such characteristic equations are particularly useful in solving differential equation s, integral equation s, and L is a {{link=linear transformation">linear transformation such as a matrix or a differential operator , and x can be a vector or a function (called an eigenvector or eigenfunction). The totality of eigenvalues for a given characteristic equation is a set. In quantum mechanics, where L is an energy operator, the eigenvalues are energy values.