eigenvalue

eigenvalue

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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eigenvalue [′ī·gən‚val·yü]

(mathematics)

The one of the scalars λ such thatT(v) = λv, whereTis a linear operator on a vector space, andvis an eigenvector. Also known as characteristic number; characteristic root; characteristic value; latent root; proper value.

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Eigenvalue (quantum mechanics)

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 Quantum mechanics

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(mathematics)

eigenvalue - The factor by which a linear transformation multiplies one of its eigenvectors.