Math - eigenvector:eigenvector

<mathematics> 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.