Interactive Eigenvector and Eigenvalue visualization

This blog post builds on my previous blog post and visualizes the eigenvectors and the eigenvalues belonging to the symmetrix input matrix. This has important applications in engineering and sciences, for example in the analysis of tension in materials, in rigid body rotations, oscillations, etc.

In the below animated and interactive illustration,

  • the yellow cross is in the directions of the eigenvectors
  • the red, semitransparent ellipsoid’s illustrates the eigenvalues: the principal axes have the same orientation as the eigenvectors, and the extents are determined by the eigenvalues
  • the blue, semitransparent sphere has the radius of the middle extent of the ellipsoid and is there only to emphasize the ellipsoid when it is almost spherical
  • the gray arrows serve the same purpose as in my previous blog post
Input matrix:


Eigenvalues:
+0.000
+0.000
+0.000


Eigenvectors:
+0.000
+0.000
+0.000
 
+0.000
+0.000
+0.000
 
+0.000
+0.000
+0.000


XYZ Euler angles:
+0.000
+0.000
+0.000
If you think you found a mistake in this blog post, or would like to suggest an improvement to this blog post, you can write me an e-mail to the address public dot michael at franzl dot name; as subject please use the prefix "Comment to blog post" and append the post title.
 
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