Ky Fan Trace Maximum Principle
Maximize captured quadratic-form trace with an orthonormal frame.
Free theory articleMaximize captured quadratic-form trace with an orthonormal frame.
Concept & interpretation
The Ky Fan Trace Maximum Principle states that for a real symmetric diagonal matrix A with descending eigenvalues, the maximum trace of Q^T*A*Q over orthonormal k-column frames Q is exactly the sum of the k largest eigenvalues.
Experiment
By adjusting the Spectrum, Frame rank, and Rotation degrees controls in the interactive module, you can observe how the frame trace varies:
- Select the Positive option for Spectrum to use the positive spectrum preset.
- Set the Frame rank to 2 to choose a 2-column frame.
- Change the Rotation degrees to 45 to evaluate the trace at this specific rotation angle.
- Observe that the Frame trace shows 5.0, which is less than or equal to the Ky Fan maximum of 7.