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 ...

We study sample covariance matrices of the form $W=(1/n)CC^{\intercal}$, where C is a k × n matrix with independent and identically distributed (i.i.d.) mean 0 ...

May’s celebrated theoretical work of the 70’s contradicted the established paradigm by demonstrating that complexity leads to instability in biological systems. Here May’s random-matrix modelling ...

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.

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, ...

A potent theory has emerged explaining a mysterious statistical law that arises throughout physics and mathematics. Imagine an archipelago where each island hosts a single tortoise species and all the ...