Cauchy Eigenvalue Interlacing

Cauchy's Eigenvalue Interlacing Theorem states that when we take a real symmetric matrix and delete one of its rows and the corresponding column, the eigenvalues of the resulting smaller principal submatrix interlace those of the original matrix.

Experiment

Try it out in the interactive module:

1. Open the Cauchy Eigenvalue Interlacing module.
2. Set the Matrix control to "Path".
3. Change the Deleted index to 1. Notice how the minor eigenvalues change to 2 and 2, and the smallest interlacing slack becomes exactly 0. The interlacing inequality is still satisfied.