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Definition of EIGENVALUE
: a scalar associated with a given linear transformation of a vector space and having the property that there is some nonzero vector which when multiplied by the scalar is equal to the vector obtained by letting the transformation operate on the vector; especially: a root of the characteristic equation of a matrix
Origin of EIGENVALUE
part translation of German Eigenwert, from eigen own, peculiar + Wert value
First Known Use: 1927
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.