# Eigenvectors

This topic is 4996 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Hello, Sometimes, when I calculate the eigenvectors of vertex cloud, I find 1 or 2 eigenvalues. So, in my OBB determination, to have 1 value means world axes(X,Y,Z). But when I only find 2 values....what can I do? Thanks a lot.

##### Share on other sites
When you have an eigenvalue of algebraic and geometric multiplicity of 2, the corresponding eigenspace is two dimensional. This space happens to be the orthogonal complement of the one-dimensional eigenspace for the other distinct eigenvalue. Any pair of unit-length and orthogonal vectors in the two-dimensional eigenspace is a valid choice.

For example, suppose your covariance matrix is Diagonal(1,1,2). An eigenvector for eigenvalue 2 is (0,0,1). Eigenvectors for eigenvalue 1 are all of the form (x,y,0), where x^2+y^2=1. The infinitely many pairs of orthogonal eigenvectors are (cos(t),sin(t),0) and (-sin(t),cos(t),0) for any angle t in [0,2*pi).

• ### What is your GameDev Story?

In 2019 we are celebrating 20 years of GameDev.net! Share your GameDev Story with us.

• 17
• 14
• 10
• 9
• 11
• ### Forum Statistics

• Total Topics
634097
• Total Posts
3015505
×