Gerschgorin Disks and Brauer's ovals of Cassini (2014)
8 days ago
- #interactive-math
- #eigenvalues
- #matrix-theory
- Interactive tool for plotting eigenvalue inclusion sets for 3x3 matrices.
- Gerschgorin's theorem provides eigenvalue bounds using diagonal entries and off-diagonal row sums.
- Brauer's ovals of Cassini improve upon Gerschgorin's bounds by considering pairs of rows.
- Ovals of Cassini are always at least as good as Gerschgorin disks for eigenvalue estimation.
- Generalizations to more than two rows do not necessarily improve bounds and may exclude eigenvalues.
- The tool uses custom JavaScript libraries for complex matrix operations and plotting.
- Source code is available on GitHub, encouraging reuse and modification.
- The project is a tribute to Professor Richard S. Varga's contributions to mathematics.