Dr. James McCaffrey of Microsoft Research presents a full-code, step-by-step tutorial on an implementation of the technique that emphasizes simplicity and ease-of-modification over robustness and ...

Inverting a matrix is one of the most common tasks in data science and machine learning. In this article I explain why inverting a matrix is very difficult and present code that you can use as-is, or ...

Matrix decomposition is an area of linear algebra which is focused on expressing a matrix as a product of matrices with prescribed properties. (Photo credit: Merino et al., 2024) Imagine discovering ...

Abstract.The full-rank LDL* decomposition of a polynomial Hermitian matrix is examined. Explicit formulae are given evaluating the coefficients of matrices 𝑙𝑖𝑗 and 𝑑𝑗𝑗. Also, a new method is ...

Let G = GLn(q), q a prime power, and let r be an odd prime not dividing q. Let s be a semisimple element of G of order prime to r and assume that r divides q°(Λ) - 1 for all elementary divisors Λ of s ...