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 well-known error estimates for the numerical computation of eigenvalues of symmetric integral equations are extended to the computation of the eigenvectors. The ...

SIAM Review contains articles that are written for a wide scientific audience. Articles include expository or survey papers focusing on important advances in applied or computational mathematics, or ...

where A is an arbitrary square numeric matrix for which eigenvalues and eigenvectors are to be calculated. The following are properties of the unsymmetric real eigenvalue problem, in which the real ...

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.

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 ...

Now assume to be symmetric with non-zero off-diagonal elements, i.e. , . Let be the eigenvalues and the normalized eigenvectors of T, i.e. We consider the inverse problem: Determine from and . It 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 ...