# eigenvalue

eigenvalue
/uy"geuhn val'yooh/, n. Math.
[1925-30; partial trans. of G Eigenwert, equiv. to eigen- characteristic, particular + Wert VALUE]

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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.

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one of a set of discrete values of a parameter, k, in an equation of the form  = , in which P is a linear operator (that is, a symbol denoting a linear operation to be performed), for which there are solutions satisfying given boundary conditions. The symbol ψ (psi) represents an eigenfunction (proper or characteristic function) belonging to that eigenvalue. The totality of eigenvalues is a set. In quantum mechanics P is frequently a Hamiltonian, or energy, operator and the eigenvalues are energy values, but operators corresponding to other dynamical variables such as total angular momentum are also used. Experimental measurements of the proper dynamical variable will yield eigenvalues.

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Universalium. 2010.

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