Pseudo-Eigenvectors of the β-Hermite Matrix Model

Each movie shows the "pseudo-eigenvectors" produced by the "shooting method" for different values of λ in (A-λI)x = 0, for a fixed matrix A. Each subgroup (set of 3) of movies uses a different matrix A drawn from the β-Hermite matrix model distribution, for β=2. If λ is a true eigenvalue, then x is a true eigenvector. If not, we get something in between true eigenvectors. The movie also displays the number of times x crosses zero (the number of sign changes in x when including the residue), which is equal to the number of eigenvalues of A greater than λ.

Normalized Pseudo-Eigenvectors

The following movies show the normalized pseudo-eigenvector as λ is shifted from the largest eigenvalue to the smallest.

100 x 100 matrix

200 x 200 matrix


Non-normalized Pseudo-Eigenvectors

The following movies show the pseudo-eigenvector computed by setting the last entry to 1 and "shooting" to solve the rest of the entries. The Y-scale is adjusted throughout the movie to keep the relevant values in frame. Again, λ is shifted from the largest eigenvalue to the smallest.

100 x 100 matrix

200 x 200 matrix


These movies were produced using MATLAB and The Berkeley MPEG Encoder.
Last updated October 26, 2006