Image: Eigenvectors-extended

Description: The transformation matrix [2112]{\displaystyle {\bigl [}{\begin{smallmatrix}2&1\\1&2\end{smallmatrix}}{\bigr ]}} preserves the direction of vectors parallel to (11){\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. These lines are represented as faint blue and violet lines, matching the associated eigenvectors. The vectors in red are not eigenvectors, therefore their direction is altered by the transformation. Notice that all 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.
Title: Eigenvectors-extended
Credit: Own work
Author: Lucas V. Barbosa
Permission: I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
Usage Terms: Public domain
License: Public domain
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