Sign in to follow this  

Eigenvectors

This topic is 4595 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

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 this post


Link to post
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).

Share this post


Link to post
Share on other sites

This topic is 4595 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

Sign in to follow this