Source : Free On-Line Dictionary of Computing

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)