Spectral certification: an interactive proof explorer
This interactive companion follows a 2×2 spectral-certification toy example from contour separation to the final operator gate and preservation of the enclosed spectral count. Its thirteen steps connect the written argument to the geometry of balls, ellipsoids, inverse bounds and uncertainty.
Open the interactive explorer or open the complete 4K overview.
Explore the argument
Use the numbered navigation to move between steps. The Geometry, Argument and Connections tabs explain the objects, the inequalities and how the steps fit together. The diagrams adapt to the available width; on a narrow screen, scroll down to see each panel.
The explorer below is hosted on this blog. For more room, use either of the links above to open it as a full page.
Reading the pictures
The contour lives in the spectral plane. The image and inverse-image diagrams describe vector spaces, while the matrix-enclosure diagrams describe matrix space. Their labels distinguish certified lower bounds, inverse upper bounds and quantities evaluated at a selected point.
The moving pictures illustrate the supplied certification argument. A sampled singular value or a rotated section does not itself certify a whole-contour minimum. The final endpoint is an abstract toy operator.