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| Keywords: Eigenvectors-extended.gif The transformation matrix <math>\bigl \begin smallmatrix 2 1\\ 1 2 \end smallmatrix \bigr</math> preserves the direction of vectors parallel to <math>\bigl \begin smallmatrix 1 \\ 1 \end smallmatrix \bigr </math> in blue and <math>\bigl \begin smallmatrix 1 \\ -1 \end smallmatrix \bigr </math> 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 own 2012-10-12 Lucas V Barbosa File Eigenvectors gif Eigenvalue problems Transformations geometry | ||||
