| eigenvector A which, when acted on by a particular , produces a scalar multiple of the original vector. The scalar in question is called the 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 on them; "are vectors", and many partial differential operators are linear transformations on the space of such functions; quantum-mechanical states "are vectors", and are linear transformations on the state space. An important theorem says, roughly, that certain linear transformations have enough eigenvectors that they form a of the whole vector states. This is why works, and why in quantum mechanics every state is a superposition of eigenstates of observables. An eigenvector is a (representative member of a) of the map on the induced by a . (1996-09-27) |
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