![The transformation matrix [ 2 1 1 2 ] {\displaystyle {\bigl [}{\begin{smallmatrix}2&1\\1&2\end{smallmatrix}}{\bigr ]}} preserves the direction of vectors parallel to ( 1 1 ) {\displaystyle {\bigl (}{\begin{smallmatrix}1\\1\end{smallmatrix}}{\bigr )}} (in blue) and ( 1 − 1 ) {\displaystyle {\bigl (}{\begin{smallmatrix}1\\-1\end{smallmatrix}}{\bigr )}} (in violet). The points that lie on the line through the origin, parallel to an eigenvector, remain on the line after the transformation. The vectors in red are not eigenvectors, therefore their direction is altered by the transformation. Notice that the blue vectors are scaled by a factor of 3. This is their associated eigenvalue. The violet vectors are not scaled, so their eigenvalue is 1.](http://upload.wikimedia.org/wikipedia/commons/0/06/Eigenvectors.gif)
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Eigenvectors.gif (300 × 300 pixels, file size: 58 KB, MIME type: image/gif, looped, 30 frames, 10 s)
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| Description |
The transformation matrix preserves the direction of vectors parallel to (in blue) and (in violet). The points that lie on the line through the origin, parallel to an eigenvector, remain on the line after the transformation. The vectors in red are not eigenvectors, therefore their direction is altered by the transformation. Notice that the blue vectors are scaled by a factor of 3. This is their associated eigenvalue. The violet vectors are not scaled, so their eigenvalue is 1. |
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| Date | |||
| Source | Own work | ||
| Author | Lucas Vieira | ||
| Permission (Reusing this file) |
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| Other versions |
Extended version showing all quadrants:  |
![{\displaystyle {\bigl [}{\begin{smallmatrix}2&1\\1&2\end{smallmatrix}}{\bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dcacd8bee0f5c4d9f5e8e3fc2c4932447e0e2aec)
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 00:34, 16 May 2012 | | 300 × 300 (58 KB) | LucasVB | More accurate version. |
| 11:37, 15 May 2012 |  | 300 × 300 (66 KB) | LucasVB | {{Information |Description=Animation depicting eigenvectors of a transformation matrix, showing how they maintain direction. |Source={{own}} |Date=2012-05-15 |Author= Kieff |Permission={{PD-self}} |other_versions= }} [[Category:Linear a... |
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