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 ...

The well-known error estimates for the numerical computation of eigenvalues of symmetric integral equations are extended to the computation of the eigenvectors. The ...

Existence and comparison theorems for eigenvalues of (k, n - k)-focal point and (k, n - k)-conjugate point problems are proved for a class of nth order linear differential equations for arbitrary n.

Eigenvalue problems are a cornerstone of modern applied mathematics, arising in diverse fields from quantum mechanics to structural engineering. At their heart, these problems seek scalar values and ...

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 ...

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 ...

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 ...