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 ...

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.

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 ...

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 ...

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 ...

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 ...