A viral health trend makes it easier to rack up extra steps, water and protein — and it comes in threes. With the "3x3 by 12 p.m." challenge, participants aim to achieve 3,000 steps, one-third of ...

M. L. Pei [Comm. ACM 5, 10 (Oct. 1962)] gave an explicit inverse for a matrix of the form M + &dgr;I, where M is an n-square matrix of ones and &dgr; is a nonzero parameter. The eigenvalues of the Pei ...

It has been known that the eigenvalues of a certain 2n × 2n matrix can be obtained by use of two smaller matrices of order n which can be easily constructed. An algorithm is given to obtain the ...

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, ...

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.

Abstract: An analytic parahermitian matrix admits in almost all cases an eigenvalue decomposition (EVD) with analytic eigenvalues and eigenvectors. We have previously defined a discrete Fourier ...

Eigenvectors are used throughout the physical and social sciences to reduce the dimension of complex problems to manageable levels and to distinguish signal from noise. Our research identifies and ...