Eigenvector - Revision history

Bradley Monk at 03:53, 27 August 2013

2013-08-27T03:53:17Z

← Older revision		Revision as of 20:53, 26 August 2013
Line 1:		Line 1:


	[[File:Eigenvectors.gif\|right\|frame\|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. The vectors in red are not eigenvectors, therefore their direction is altered by the transformation. ]]		[[File:Eigenvectors.gif\|right\|frame\|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. The vectors in red are not eigenvectors, therefore their direction is altered by the transformation. ]]

Bradley Monk at 03:37, 27 August 2013

2013-08-27T03:37:59Z

← Older revision		Revision as of 20:37, 26 August 2013
Line 1:		Line 1:


	[[File:Eigenvectors.gif\|right\|frame\|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. The vectors in red are not eigenvectors, therefore their direction is altered by the transformation. ]]		[[File:Eigenvectors.gif\|right\|frame\|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. The vectors in red are not eigenvectors, therefore their direction is altered by the transformation. ]]

Bradley Monk at 03:14, 27 August 2013

2013-08-27T03:14:05Z

← Older revision		Revision as of 20:14, 26 August 2013
Line 1:		Line 1:


	[[File:Eigenvectors.gif\|right\|frame\|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. The vectors in red are not eigenvectors, therefore their direction is altered by the transformation~~. See also: [[:File:Eigenvectors-extended.gif\|An extended version, showing all four quadrants]]~~.]]		[[File:Eigenvectors.gif\|right\|frame\|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. The vectors in red are not eigenvectors, therefore their direction is altered by the transformation. ]]





			[[File:Eigenvectors-extended.gif\|thumb\|left\|frame\|showing all four quadrants]].

Bradley Monk: Created page with " [[File:Eigenvectors.gif|right|frame|The transformation matrix $\bigl[ \begin{smallmatrix} 2 & 1\\ 1 & 2 \end{smallmatrix} \bigr]$ preserves the direction of vecto..."

2013-08-27T02:04:34Z

Created page with " [[File:Eigenvectors.gif|right|frame|The transformation matrix <math>\bigl[ \begin{smallmatrix} 2 & 1\\ 1 & 2 \end{smallmatrix} \bigr]</math> preserves the direction of vecto..."

New page

[[File:Eigenvectors.gif|right|frame|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. The vectors in red are not eigenvectors, therefore their direction is altered by the transformation. See also: [[:File:Eigenvectors-extended.gif|An extended version, showing all four quadrants]].]]

[[Category:Math]] [[Category:Computational]]

Eigenvector - Revision history

Bradley Monk at 03:53, 27 August 2013

Bradley Monk at 03:37, 27 August 2013

Bradley Monk at 03:14, 27 August 2013

Bradley Monk: Created page with " [[File:Eigenvectors.gif|right|frame|The transformation matrix \bigl[ \begin{smallmatrix} 2 & 1\\ 1 & 2 \end{smallmatrix} \bigr] preserves the direction of vecto..."

Bradley Monk: Created page with " [[File:Eigenvectors.gif|right|frame|The transformation matrix $\bigl[ \begin{smallmatrix} 2 & 1\\ 1 & 2 \end{smallmatrix} \bigr]$ preserves the direction of vecto..."