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Eigenvalue-Eigenstate-Eigenvector

In the practice of pure and applied mathematics, linear transformations are often applied to bring a system out of one matrix into another for the purpose of applying different functions to the problem. The eigenvector of a given linear transformation is that vector which is *not* changed by that transformation. In the same way, an eigenvalue is a magnitude proportion of the vector that does *not* change in the transformation, and the eigenspace of a transformation is the set of all eigenvectors (plus the zero vector) that have the same eigenvalue. Thus an eigenspace is a subspace of a total vector space.

Many values in mathematics can be treated as vectors: quantum states, frequencies, functions, harmonics, etc. Vector directions assigned to such values may be abstract, but so long as the direction does not change during a linear transformation, "eigen" can be used to describe the value - eigenfunction, eigenfrequency, eigenstate, etc.

Web Resources On Eigenvalue-Eigenstate-Eigenvector

Eigenvalue, eigenvector and eigenspace (Wikipedia)
Online Calculator for Eigenvalues and Eigenvectors
The universe as an eigenstate: spacetime paths and decoherence

Book Resources On Eigenvalue-Eigenstate-Eigenvector

Hp-48G/Gx Investigations in Mathematics by Donald R. Latrve, Donald L. Kreider, T.G. Proctor.
Principles of Linear Systems by Philip E. Sarachik
The Nature of Space and Time by Stephen Hawking and Roger Penrose

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