Eigenvalue optimisation problems involve identifying design or material configurations that either maximise or minimise the eigenvalues associated with differential operators under given boundary ...

Eigenvalue problems on Riemannian manifolds lie at the heart of modern geometric analysis, bridging the gap between differential geometry and partial differential equations. In this framework, the ...

There are two main techniques to implement PCA. The first technique, sometimes called classical, computes eigenvalues and eigenvectors from a covariance matrix derived from the source data. The second ...

Transforming a dataset into one with fewer columns is more complicated than it might seem, explains Dr. James McCaffrey of Microsoft Research in this full-code, step-by-step machine learning tutorial.