See Also: eigenvalue(encyclopedia)

eigenvalue (sh)




In mathematical analysis, one of a set of discrete values of a parameter, k, in an equation of the form Lx = kx.

Such characteristic equations are particularly useful in solving differential equations, integral equations, and systems of equations. In the equation, L is a 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.