Abstract Let A be an n × n Hermitian matrix and A = UΛUH be its spectral decomposition, where U is a unitary matrix of order n and Λ is a diagonal matrix. In this note we present the perturbation ...

where A is an arbitrary square numeric matrix for which eigenvalues and eigenvectors are to be calculated. The following are properties of the unsymmetric real eigenvalue problem, in which the real ...

Random Matrix Theory (RMT) has emerged as an indispensable framework for understanding the statistical properties of matrices whose entries are determined by probabilistic processes. Initially ...

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, ...

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 ...

This paper considers the sensitivity of the eigenvalues and eigenvectors of the generalized matrix eigenvalue problem Ax = λ Bx to perturbations of A and B. The ...

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 ...

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 ...