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The word "simply" should rarely be used in maths |
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[[Image:Mona Lisa with eigenvector.png|thumb|270px|Fig. 1. This has nothing to do with eigenthingies. In this [[shear (mathematics)|shear]] transformation of the [[Mona Lisa]], the picture was deformed in such a way that its central vertical axis (red vector) was not modified, but the diagonal vector (blue) has changed direction. Hence the red vector is an <font color="#CC1111">'''eigenvector'''</font> of the transformation and the blue vector is <font color="darkblue">not</font>. Since the red vector was neither stretched nor compressed, its '''eigenvalue''' is 1. All vectors with the same vertical direction - i.e., parallel to this vector - are also eigenvectors, with the same eigenvalue. Together with the zero-vector, they form the '''eigenspace''' for this eigenvalue.]]
In [[mathematics]], a [[Vector (spatial)|vector]] may be thought of as an arrow. It has a length, called its ''magnitude'', and it points in some particular ''direction''. A [[linear transformation]] may be considered to operate on a vector to change it, usually changing both its magnitude and its direction. An {{Audio|De-eigenvector.ogg|'''eigenvector'''}} of a given linear transformation is a vector which is multiplied by a constant called the {{Audio-nohelp|De-eigenvalue.ogg|'''eigenvalue'''}} during that transformation. The direction of the eigenvector is either unchanged by that transformation (for positive eigenvalues) or reversed (for negative eigenvalues).
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