Eigenvalue

(mathematics) The one of the scalars λ such that T(v) = λv, where T is a linear operator on a vector space, and v is an eigenvector. Also known as characteristic number; characteristic root; characteristic value; latent root; proper value.

If an equation containing a variable parameter possesses nontrivial solutions only for certain special values of the parameter, these solutions are called eigenfunctions and the special values are called eigenvalues.

The eigenfunction-eigenvalue relation is of particular importance in quantum mechanics because of its prominence in the equations which relate the mathematical formalism of the theory with physical results. See also Quantum mechanics.