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An eigenvector of a linear transformation (operator) is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it.



In applications in the natural sciences the eigenvector, which belongs to an eigenvalue, is also called an eigenstate because it concerns a special state of the described system.



The use of the prefix "eigen" for characteristic quantities can be traced back to a 1904 publication by the German mathematician David Hilbert.

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