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, ...

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.

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 ...

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 ...

Seems like GE on a 2x2 matrix should be pretty darn fast.... especially if you use scalar * vector type operations.

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 ...

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 ...