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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 ...

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, ...

The purpose of principal component analysis is to derive a small number of independent linear combinations (principal components) of a set of variables that retain as much of the information in the ...

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 ...

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.

When a regressor is nearly a linear combination of other regressors in the model, the affected estimates are unstable and have high standard errors. This problem is called collinearity or ...