[1] : The Free On-line Dictionary of Computing (27 SEP 03)

eigenvector
     
         a vector which, when acted on by a particular
        linear transformation, produces a scalar multiple of the
        original vector.  the scalar in question is called the
        eigenvalue corresponding to this eigenvector.
     
        it should be noted that "vector" here means "element of a
        vector space" which can include many mathematical entities.
        ordinary vectors are elements of a vector space, and
        multiplication by a matrix is a linear transformation on
        them; smooth functions "are vectors", and many partial
        differential operators are linear transformations on the space
        of such functions; quantum-mechanical states "are vectors",
        and observables are linear transformations on the state
        space.
     
        an important theorem says, roughly, that certain linear
        transformations have enough eigenvectors that they form a
        basis of the whole vector states.  this is why fourier
        analysis works, and why in quantum mechanics every state is a
        superposition of eigenstates of observables.
     
        an eigenvector is a representative member of a fixed point
        of the map on the projective plane induced by a linear
        map.
     
        1996-09-27
     
     
see also:
vector linear transformation eigenvalue smooth functions observables basis 
fourier analysis fixed point projective plane linear map 

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Eigenvector, definition of term: Eigenvector
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