In mathematical analysis, one of a set of discrete values of a parameter, math.k, in an equation of the form math.Lx = math.kx. Such characteristic equations are particularly useful in solving differential equations, integral equations, and systems of equations. In the equation, math.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 math.L is an energy operator, the eigenvalues are energy values.
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