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