Symmetric Eigenvalue Deflation

Symmetric eigenvalue deflation is a technique used in numerical linear algebra to find multiple eigenvalues of a symmetric matrix. Once an eigenvalue and its corresponding eigenvector are found, the matrix can be modified (deflated) so that the found eigenvalue is shifted, while the other eigenvalues and eigenvectors remain unchanged.

Experiment

Use the Symmetric Eigenvalue Deflation interactive module to explore this concept.

1. Select 1 for the Subtraction factor.
2. Observe that the Removed eigenvalue amount is 5.
3. Verify that the Dominant remaining eigenvalue is exactly 2.
4. Select 1.5 for the Subtraction factor.
5. Observe that the Removed eigenvalue amount becomes 7.5.
6. Notice that the Dominant remaining eigenvalue is now -2.5, which has a magnitude of 2.5.