If the application of an operator to a function gives back the original function multiplied by some constant, then this constant is known as the eigenvalue of that function. In quantum mechanics, eigenvalues often correspond to observables.
and eigenvector. If a (scalar) value, t, satisfies Ax = tx for some vector, x not= 0, it is an eigenvalue of the matrix A, and x is an eigenvector. In mathematical programming this arises in the context of convergence analysis, where A is the hessian of some merit function, such as the objective or Lagrangian.