Eigenvalue problems occupy a central role in Riemannian geometry, providing profound insights into the interplay between geometry and analysis. At their core, these problems involve the study of ...

Usually the way things work is that mathematicians make math discoveries, and physicists borrow and adapt those ideas to explain the universe. But three physicists at the University of Chicago and two ...

Correction: The original version of this article incorrectly stated that eigenvalues are the magnitudes of eigenvectors. In fact, eigenvalues are scalars that are multiplied with eigenvectors. This ...

This video explains eigenvalues and eigenvectors in a fresh, intuitive way, focusing on meaning and visualization rather than memorized formulas. Learn how they describe transformation behavior, why ...

Principal components analysis is perhaps the most widely used method for exploring multivariate data. In this paper, we propose a variability plot composed of measures on the stability of each ...

This article presents a from-scratch C# implementation of the second technique: using SVD to compute eigenvalues and eigenvectors from the standardized source data. If you're not familiar with PCA, ...

Network analysis begins with data that describes the set of relationships among the members of a system. The goal of analysis is to obtain from the low-level relational data a higher-level description ...