Here are three examples that we will consider. In each case, we have pre-computed the eigenvalues and eigenvectors (check them yourself). \[ A = \begin{bmatrix} 2 & 2 ...

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 ...

After breakfast one morning in August, the mathematician Terence Tao opened an email from three physicists he didn’t know. The trio explained that they’d stumbled across a simple formula that, if true ...

Ecologists are fascinated by the prevalence of nestedness in biogeographic and community data, where it is thought to promote biodiversity in mutualistic systems. Traditionally, nestedness has been ...

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.