mathematics A
vector which, when acted on by a particular
original vector. The scalar in question is called the
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
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
Fourieranalysis 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(1996-09-27)