We prove trace identities for commutators of operators, which are used to derive sum rules and sharp universal bounds for the eigenvalues of periodic Schrödinger operators and Schrödinger operators on ...

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 ...

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, ...

Eigensensitivity analysis addresses how the spectral properties of damped systems—specifically, the eigenvalues and eigenvectors—respond to variations in system parameters. This analytical approach is ...

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 ...