I. “+ˌ- noun
Etymology: part translation of German eigenwert, from eigen- + wert value
: any of the permissible values of a parameter in an eigenfunction (as the discrete values of the energy in the solution of the Schrödinger wave equation)
II. noun
: 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
if T(v) = λv , where T is a linear transformation, v is a nonzero vector, and λ is a scalar, then λ is an eigenvalue of T , and v is an eigenvector of T corresponding to λ
specifically : a root of the characteristic equation of a matrix